A topological model for the coloured Jones polynomials-Reference-Cited by-同舟云学术

A topological model for the coloured Jones polynomials

Published:2022-04-30 Issue:3 Volume:28 Page:
ISSN:1022-1824
Container-title:Selecta Mathematica
language:en
Short-container-title:Sel. Math. New Ser.

Author:

Anghel Cristina Ana-Maria

Abstract

AbstractIn this paper we will present a homological model for Coloured Jones Polynomials. For each colour

$$N \in {\mathbb {N}}$$

N ∈ N , we will describe the invariant

$$J_N(L,q)$$

J N ( L , q ) as a graded intersection pairing of certain homology classes in a covering of a configuration space on the punctured disc. This construction is based on the Lawrence representation and a result due to Kohno that relates quantum representations and homological representations of the braid groups.

Publisher

Springer Science and Business Media LLC

Subject

General Physics and Astronomy,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00029-022-00772-4.pdf

Reference23 articles.

1. Anghel, C.: Coloured Jones and Alexander polynomials as topological intersections of cycles in configuration spaces. math.GT Submitted, 47 p (2020) arXiv: 2002.09390

2. Anghel, C.: $$U_q(sl(2))-$$quantum invariants unified via intersections of embedded Lagrangians. math.GT, Submitted, 24 p (2020). arXiv: 2010.05890

3. Anghel, C.: Witten–Reshetikhin–Turaev invariants for $$3$$-manifolds from Lagrangian intersections in configuration spaces. Submitted, 24 p (2021). arXiv: 2104.02049

4. Bigelow, S.: A homological definition of the Jones polynomial. In: Invariants of knots and 3-manifolds (Kyoto, 2001), volume 4 of Geom. Topol. Monogr., pp. 29–41. Geom. Topol. Publ., Coventry (2002)

5. Bigelow, S.: Braid groups are linear. J. Am. Math. Soc. 14, 471–486 (2001)

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Unified invariant of knots from homological braid action on Verma modules;Proceedings of the London Mathematical Society;2024-05

2. A topological model for the coloured Alexander invariants;Topology and its Applications;2023-04