Connection Between Knot Theory and Number Theory
$begingroup$
Is there any connection between knot theory and number theory in any aspects?
Does anybody know any book that is about knot theory and number theory?
reference-request arithmetic-geometry algebraic-number-theory knot-theory
edited Mar 19 at 15:05
Sean Lawton
3,96622247
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Is there any connection between knot theory and number theory in any aspects?
Does anybody know any book that is about knot theory and number theory?
reference-request arithmetic-geometry algebraic-number-theory knot-theory
edited Mar 19 at 15:05
Sean Lawton
3,96622247
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
4
$begingroup$
Welcome new contributor. Perhaps you are looking for Mazur's dictionary: neverendingbooks.org/mazurs-dictionary
$endgroup$
– Jason Starr
Mar 19 at 13:15
6
$begingroup$
The answers so far are about the analogy between primes and knots, which typically takes inspiration from knot theory to try to do some number theory. There’s some small amount of work going the other direction, notably by Alison Miller (math.harvard.edu/~abmiller).
$endgroup$
– Daniel Litt
Mar 19 at 13:59
$begingroup$
@DanielLitt thank you for promoting research outside the mainstream understanding.
$endgroup$
– Matt Cuffaro
Mar 19 at 14:37
add a comment |
$begingroup$
Is there any connection between knot theory and number theory in any aspects?
Does anybody know any book that is about knot theory and number theory?
reference-request arithmetic-geometry algebraic-number-theory knot-theory
edited Mar 19 at 15:05
Sean Lawton
3,96622247
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Is there any connection between knot theory and number theory in any aspects?
Does anybody know any book that is about knot theory and number theory?
reference-request arithmetic-geometry algebraic-number-theory knot-theory
reference-request arithmetic-geometry algebraic-number-theory knot-theory
edited Mar 19 at 15:05
Sean Lawton
3,96622247
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 19 at 15:05
Sean Lawton
3,96622247
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 19 at 15:05
Sean Lawton
3,96622247
edited Mar 19 at 15:05
Sean Lawton
3,96622247
edited Mar 19 at 15:05
Sean Lawton
3,96622247
3,96622247
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
243
243
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
fsociety_1729 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
4
$begingroup$
Welcome new contributor. Perhaps you are looking for Mazur's dictionary: neverendingbooks.org/mazurs-dictionary
$endgroup$
– Jason Starr
Mar 19 at 13:15
6
$begingroup$
The answers so far are about the analogy between primes and knots, which typically takes inspiration from knot theory to try to do some number theory. There’s some small amount of work going the other direction, notably by Alison Miller (math.harvard.edu/~abmiller).
$endgroup$
– Daniel Litt
Mar 19 at 13:59
$begingroup$
@DanielLitt thank you for promoting research outside the mainstream understanding.
$endgroup$
– Matt Cuffaro
Mar 19 at 14:37
add a comment |
4
$begingroup$
Welcome new contributor. Perhaps you are looking for Mazur's dictionary: neverendingbooks.org/mazurs-dictionary
$endgroup$
– Jason Starr
Mar 19 at 13:15
6
$begingroup$
The answers so far are about the analogy between primes and knots, which typically takes inspiration from knot theory to try to do some number theory. There’s some small amount of work going the other direction, notably by Alison Miller (math.harvard.edu/~abmiller).
$endgroup$
– Daniel Litt
Mar 19 at 13:59
$begingroup$
@DanielLitt thank you for promoting research outside the mainstream understanding.
$endgroup$
– Matt Cuffaro
Mar 19 at 14:37
4
4
$begingroup$
Welcome new contributor. Perhaps you are looking for Mazur's dictionary: neverendingbooks.org/mazurs-dictionary
$endgroup$
– Jason Starr
Mar 19 at 13:15
$begingroup$
Welcome new contributor. Perhaps you are looking for Mazur's dictionary: neverendingbooks.org/mazurs-dictionary
$endgroup$
– Jason Starr
Mar 19 at 13:15
6
6
$begingroup$
The answers so far are about the analogy between primes and knots, which typically takes inspiration from knot theory to try to do some number theory. There’s some small amount of work going the other direction, notably by Alison Miller (math.harvard.edu/~abmiller).
$endgroup$
– Daniel Litt
Mar 19 at 13:59
$begingroup$
The answers so far are about the analogy between primes and knots, which typically takes inspiration from knot theory to try to do some number theory. There’s some small amount of work going the other direction, notably by Alison Miller (math.harvard.edu/~abmiller).
$endgroup$
– Daniel Litt
Mar 19 at 13:59
$begingroup$
@DanielLitt thank you for promoting research outside the mainstream understanding.
$endgroup$
– Matt Cuffaro
Mar 19 at 14:37
$begingroup$
@DanielLitt thank you for promoting research outside the mainstream understanding.
$endgroup$
– Matt Cuffaro
Mar 19 at 14:37
add a comment |
5 Answers
5
active
oldest
votes
$begingroup$
The question seems very general, but the first book to come to mind is this:
The Arithmetic of Hyperbolic 3-Manifolds, with C. Maclachlan, Graduate Text in Math. 219, Springer-Verlag (2003)
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
$endgroup$
add a comment |
$begingroup$
I recommend Chao Li/Charmaine Sia's notes for a brisk and illustrated overview of the ever-growing MKR dictionary detailed in Knots and Primes. The first three or so chapters of the source book is rather accessible.
For the MKR dictionary, refer to the link in comments.
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
$endgroup$
1
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
add a comment |
$begingroup$
I am not at all an expert in these matters, but there seems to be recent developments in this area around the work of Minhyong Kim and collaborators. See in particular:
- https://arxiv.org/abs/1706.03336
- https://arxiv.org/abs/1510.05818
- https://arxiv.org/abs/1609.03012
- https://arxiv.org/abs/1712.07602
Since the classic article by Witten,
Chern-Simons gauge theory from physics is well known to be related to knot theory. My understanding is this work by Kim and collaborators aims at developing an arithmetic analogue of this theory.
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
$endgroup$
add a comment |
$begingroup$
Currently, the most complete book presenting the connections between knot theory and number theory is "Knots and Primes. An Introduction to Arithmetic Topology" by Masanori Morishita (Springer, 2012). (It also presents much of the needed prerequisites, so it should be the first choice for somebody serious about self-studying the subject.)
If you feel confident enough that you already know the basics, it might be useful to take a look at "Primes and Knots" edited by Toshitake Kohno and Masanori Morishita (AMS, 2006). It contains the proceedings of two 2003 conferences on this topic and closely related ones (and, strangely, it is currently freely available, so grab it legally while you can!).
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
$endgroup$
add a comment |
$begingroup$
I recommended look lower link.
http://www.math.columbia.edu/~chaoli/tutorial2012/KnotsAndPrimes.html
answered Mar 21 at 12:38
husseinhussein
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
add a comment |
Your Answer
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5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The question seems very general, but the first book to come to mind is this:
The Arithmetic of Hyperbolic 3-Manifolds, with C. Maclachlan, Graduate Text in Math. 219, Springer-Verlag (2003)
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
$endgroup$
add a comment |
$begingroup$
The question seems very general, but the first book to come to mind is this:
The Arithmetic of Hyperbolic 3-Manifolds, with C. Maclachlan, Graduate Text in Math. 219, Springer-Verlag (2003)
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
$endgroup$
add a comment |
$begingroup$
The question seems very general, but the first book to come to mind is this:
The Arithmetic of Hyperbolic 3-Manifolds, with C. Maclachlan, Graduate Text in Math. 219, Springer-Verlag (2003)
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
$endgroup$
The question seems very general, but the first book to come to mind is this:
The Arithmetic of Hyperbolic 3-Manifolds, with C. Maclachlan, Graduate Text in Math. 219, Springer-Verlag (2003)
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
answered Mar 19 at 13:20
Sean LawtonSean Lawton
3,96622247
3,96622247
add a comment |
add a comment |
$begingroup$
I recommend Chao Li/Charmaine Sia's notes for a brisk and illustrated overview of the ever-growing MKR dictionary detailed in Knots and Primes. The first three or so chapters of the source book is rather accessible.
For the MKR dictionary, refer to the link in comments.
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
$endgroup$
1
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
add a comment |
$begingroup$
I recommend Chao Li/Charmaine Sia's notes for a brisk and illustrated overview of the ever-growing MKR dictionary detailed in Knots and Primes. The first three or so chapters of the source book is rather accessible.
For the MKR dictionary, refer to the link in comments.
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
$endgroup$
1
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
add a comment |
$begingroup$
I recommend Chao Li/Charmaine Sia's notes for a brisk and illustrated overview of the ever-growing MKR dictionary detailed in Knots and Primes. The first three or so chapters of the source book is rather accessible.
For the MKR dictionary, refer to the link in comments.
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
$endgroup$
I recommend Chao Li/Charmaine Sia's notes for a brisk and illustrated overview of the ever-growing MKR dictionary detailed in Knots and Primes. The first three or so chapters of the source book is rather accessible.
For the MKR dictionary, refer to the link in comments.
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
edited Mar 19 at 13:41
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
answered Mar 19 at 13:35
Matt CuffaroMatt Cuffaro
160116
160116
1
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
add a comment |
1
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
1
1
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
$begingroup$
An alternative link for Li and Sia's notes, in case the above dies, is under Li's page at Columbia University.
$endgroup$
– Alex M.
Mar 21 at 18:03
add a comment |
$begingroup$
I am not at all an expert in these matters, but there seems to be recent developments in this area around the work of Minhyong Kim and collaborators. See in particular:
- https://arxiv.org/abs/1706.03336
- https://arxiv.org/abs/1510.05818
- https://arxiv.org/abs/1609.03012
- https://arxiv.org/abs/1712.07602
Since the classic article by Witten,
Chern-Simons gauge theory from physics is well known to be related to knot theory. My understanding is this work by Kim and collaborators aims at developing an arithmetic analogue of this theory.
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
$endgroup$
add a comment |
$begingroup$
I am not at all an expert in these matters, but there seems to be recent developments in this area around the work of Minhyong Kim and collaborators. See in particular:
- https://arxiv.org/abs/1706.03336
- https://arxiv.org/abs/1510.05818
- https://arxiv.org/abs/1609.03012
- https://arxiv.org/abs/1712.07602
Since the classic article by Witten,
Chern-Simons gauge theory from physics is well known to be related to knot theory. My understanding is this work by Kim and collaborators aims at developing an arithmetic analogue of this theory.
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
$endgroup$
add a comment |
$begingroup$
I am not at all an expert in these matters, but there seems to be recent developments in this area around the work of Minhyong Kim and collaborators. See in particular:
- https://arxiv.org/abs/1706.03336
- https://arxiv.org/abs/1510.05818
- https://arxiv.org/abs/1609.03012
- https://arxiv.org/abs/1712.07602
Since the classic article by Witten,
Chern-Simons gauge theory from physics is well known to be related to knot theory. My understanding is this work by Kim and collaborators aims at developing an arithmetic analogue of this theory.
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
$endgroup$
I am not at all an expert in these matters, but there seems to be recent developments in this area around the work of Minhyong Kim and collaborators. See in particular:
- https://arxiv.org/abs/1706.03336
- https://arxiv.org/abs/1510.05818
- https://arxiv.org/abs/1609.03012
- https://arxiv.org/abs/1712.07602
Since the classic article by Witten,
Chern-Simons gauge theory from physics is well known to be related to knot theory. My understanding is this work by Kim and collaborators aims at developing an arithmetic analogue of this theory.
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12870
11.1k12870
add a comment |
add a comment |
$begingroup$
Currently, the most complete book presenting the connections between knot theory and number theory is "Knots and Primes. An Introduction to Arithmetic Topology" by Masanori Morishita (Springer, 2012). (It also presents much of the needed prerequisites, so it should be the first choice for somebody serious about self-studying the subject.)
If you feel confident enough that you already know the basics, it might be useful to take a look at "Primes and Knots" edited by Toshitake Kohno and Masanori Morishita (AMS, 2006). It contains the proceedings of two 2003 conferences on this topic and closely related ones (and, strangely, it is currently freely available, so grab it legally while you can!).
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
$endgroup$
add a comment |
$begingroup$
Currently, the most complete book presenting the connections between knot theory and number theory is "Knots and Primes. An Introduction to Arithmetic Topology" by Masanori Morishita (Springer, 2012). (It also presents much of the needed prerequisites, so it should be the first choice for somebody serious about self-studying the subject.)
If you feel confident enough that you already know the basics, it might be useful to take a look at "Primes and Knots" edited by Toshitake Kohno and Masanori Morishita (AMS, 2006). It contains the proceedings of two 2003 conferences on this topic and closely related ones (and, strangely, it is currently freely available, so grab it legally while you can!).
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
$endgroup$
add a comment |
$begingroup$
Currently, the most complete book presenting the connections between knot theory and number theory is "Knots and Primes. An Introduction to Arithmetic Topology" by Masanori Morishita (Springer, 2012). (It also presents much of the needed prerequisites, so it should be the first choice for somebody serious about self-studying the subject.)
If you feel confident enough that you already know the basics, it might be useful to take a look at "Primes and Knots" edited by Toshitake Kohno and Masanori Morishita (AMS, 2006). It contains the proceedings of two 2003 conferences on this topic and closely related ones (and, strangely, it is currently freely available, so grab it legally while you can!).
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
$endgroup$
Currently, the most complete book presenting the connections between knot theory and number theory is "Knots and Primes. An Introduction to Arithmetic Topology" by Masanori Morishita (Springer, 2012). (It also presents much of the needed prerequisites, so it should be the first choice for somebody serious about self-studying the subject.)
If you feel confident enough that you already know the basics, it might be useful to take a look at "Primes and Knots" edited by Toshitake Kohno and Masanori Morishita (AMS, 2006). It contains the proceedings of two 2003 conferences on this topic and closely related ones (and, strangely, it is currently freely available, so grab it legally while you can!).
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
answered Mar 20 at 18:03
Alex M.Alex M.
2,49641633
2,49641633
add a comment |
add a comment |
$begingroup$
I recommended look lower link.
http://www.math.columbia.edu/~chaoli/tutorial2012/KnotsAndPrimes.html
answered Mar 21 at 12:38
husseinhussein
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
add a comment |
$begingroup$
I recommended look lower link.
http://www.math.columbia.edu/~chaoli/tutorial2012/KnotsAndPrimes.html
answered Mar 21 at 12:38
husseinhussein
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
add a comment |
$begingroup$
I recommended look lower link.
http://www.math.columbia.edu/~chaoli/tutorial2012/KnotsAndPrimes.html
answered Mar 21 at 12:38
husseinhussein
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I recommended look lower link.
http://www.math.columbia.edu/~chaoli/tutorial2012/KnotsAndPrimes.html
answered Mar 21 at 12:38
husseinhussein
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Mar 21 at 12:38
husseinhussein
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Mar 21 at 12:38
husseinhussein
191
answered Mar 21 at 12:38
husseinhussein
191
191
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
hussein is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
add a comment |
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
It has already been mentioned by Matt Cufaro in his answer, just with a different URL.
$endgroup$
– Alex M.
Mar 21 at 17:59
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
$begingroup$
your right. I forgot his answers.
$endgroup$
– hussein
Mar 21 at 18:01
add a comment |
fsociety_1729 is a new contributor. Be nice, and check out our Code of Conduct.
fsociety_1729 is a new contributor. Be nice, and check out our Code of Conduct.
fsociety_1729 is a new contributor. Be nice, and check out our Code of Conduct.
fsociety_1729 is a new contributor. Be nice, and check out our Code of Conduct.
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4
$begingroup$
Welcome new contributor. Perhaps you are looking for Mazur's dictionary: neverendingbooks.org/mazurs-dictionary
$endgroup$
– Jason Starr
Mar 19 at 13:15
6
$begingroup$
The answers so far are about the analogy between primes and knots, which typically takes inspiration from knot theory to try to do some number theory. There’s some small amount of work going the other direction, notably by Alison Miller (math.harvard.edu/~abmiller).
$endgroup$
– Daniel Litt
Mar 19 at 13:59
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@DanielLitt thank you for promoting research outside the mainstream understanding.
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– Matt Cuffaro
Mar 19 at 14:37