Cluster C*-algebras and knot polynomials
Operator Algebras
2016-03-04 v1 Geometric Topology
Representation Theory
Abstract
We construct a representation of the braid groups in a cluster C*-algebra coming from a triangulation of the Riemann surface S with one or two cusps. It is shown that the Laurent polynomials attached to the K-theory of such an algebra are topological invariants of the closure of braids. In particular, the Jones and HOMFLY polynomials of a knot correspond to the case S being a sphere with two cusps and a torus with one cusp, respectively.
Keywords
Cite
@article{arxiv.1603.01180,
title = {Cluster C*-algebras and knot polynomials},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:1603.01180},
year = {2016}
}
Comments
20 pages, 3 figures