2016/03/03 by Igor Nikolaev, Nikolaev, Igor
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.GT #math.OA #math.RT
paper · pdf · doi:10.48550/arxiv.1603.01180
20 pages, 3 figures
arxiv created 2016/03/03 · openalex publication_date 2016/03/03 · arxiv updated 2016/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.