Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)

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Knot-quiver correspondence: a brief review

Authors
Piotr Kucharski1, Dmitry Noshchenko2, *
1Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland
2School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin, D04 C932, Ireland
*Corresponding author. Email: dsnoshchenko@stp.dias.ie
Corresponding Author
Dmitry Noshchenko
Available Online 17 July 2025.
DOI
10.2991/978-94-6463-789-2_3How to use a DOI?
Keywords
Knots; quivers; motivic Donaldson-Thomas invariants; permutohedra; unlinking; FK invariants; 3-dimensional topology
Abstract

This note is an overview of the knot-quiver correspondence, which relates symmetric quivers and their partition functions, a.k.a. motivic Donaldson-Thomas generating series, to quantum invariants of knots and links in S(For the reader unfamiliar with knot theory, we refer to a classic book by Dale Rolfsen [1]).

Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
Series
Advances in Physics Research
Publication Date
17 July 2025
ISBN
978-94-6463-789-2
ISSN
2352-541X
DOI
10.2991/978-94-6463-789-2_3How to use a DOI?
Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Piotr Kucharski
AU  - Dmitry Noshchenko
PY  - 2025
DA  - 2025/07/17
TI  - Knot-quiver correspondence: a brief review
BT  - Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
PB  - Atlantis Press
SP  - 19
EP  - 33
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-789-2_3
DO  - 10.2991/978-94-6463-789-2_3
ID  - Kucharski2025
ER  -