Connection Between Knot Theory and Number TheoryProbabilistic knot theoryCan you characterize the group of transformations of knot diagrams which preserve the knot embedding?On connection between Knot theory and Operator algebraKnot theory without planar diagrams?What is knot contact homology?Unknotting number of knot diagramsDescriptive Complexity of Knot EquivalenceIs a “knot knot” or “double knot” a thing in knot theory?Applications of arithmetic topology to number theoryBraid group and knot group
Connection Between Knot Theory and Number Theory
Probabilistic knot theoryCan you characterize the group of transformations of knot diagrams which preserve the knot embedding?On connection between Knot theory and Operator algebraKnot theory without planar diagrams?What is knot contact homology?Unknotting number of knot diagramsDescriptive Complexity of Knot EquivalenceIs a “knot knot” or “double knot” a thing in knot theory?Applications of arithmetic topology to number theoryBraid group and knot group
$begingroup$
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
4,26422351
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
$endgroup$
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
4,26422351
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
$endgroup$
5
$begingroup$
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
4,26422351
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
$endgroup$
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
4,26422351
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
edited Mar 19 at 15:05
Sean Lawton
4,26422351
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
edited Mar 19 at 15:05
Sean Lawton
4,26422351
edited Mar 19 at 15:05
Sean Lawton
4,26422351
edited Mar 19 at 15:05
Sean Lawton
4,26422351
4,26422351
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
asked Mar 19 at 13:12
fsociety_1729fsociety_1729
293
293
5
$begingroup$
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 |
5
$begingroup$
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
5
5
$begingroup$
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
4,26422351
$endgroup$
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 |
$begingroup$
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.
2,52441633
$endgroup$
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
11.1k12871
$endgroup$
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
$endgroup$
$begingroup$
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
4,26422351
$endgroup$
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
4,26422351
$endgroup$
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
4,26422351
$endgroup$
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
4,26422351
answered Mar 19 at 13:20
Sean LawtonSean Lawton
4,26422351
answered Mar 19 at 13:20
Sean LawtonSean Lawton
4,26422351
answered Mar 19 at 13:20
Sean LawtonSean Lawton
4,26422351
4,26422351
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 |
$begingroup$
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.
2,52441633
$endgroup$
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.
2,52441633
$endgroup$
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.
2,52441633
$endgroup$
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.
2,52441633
answered Mar 20 at 18:03
Alex M.Alex M.
2,52441633
answered Mar 20 at 18:03
Alex M.Alex M.
2,52441633
answered Mar 20 at 18:03
Alex M.Alex M.
2,52441633
2,52441633
add a comment |
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
11.1k12871
$endgroup$
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
11.1k12871
$endgroup$
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
11.1k12871
$endgroup$
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
11.1k12871
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12871
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12871
answered Mar 19 at 14:44
Abdelmalek AbdesselamAbdelmalek Abdesselam
11.1k12871
11.1k12871
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
$endgroup$
$begingroup$
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
$endgroup$
$begingroup$
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
$endgroup$
I recommended look lower link.
http://www.math.columbia.edu/~chaoli/tutorial2012/KnotsAndPrimes.html
answered Mar 21 at 12:38
husseinhussein
191
answered Mar 21 at 12:38
husseinhussein
191
answered Mar 21 at 12:38
husseinhussein
191
answered Mar 21 at 12:38
husseinhussein
191
191
$begingroup$
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 |
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$begingroup$
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