A polynomial defined by the SL(2;C)-Reidemeister torsion for a homology 3-sphere obtained by a Dehn surgery along a (2p,q)-torus knot

2015/06/05 by Teruaki Kitano, Kitano, Teruaki
Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.1506.01774

openalex publication_date 2015/06/05 · arxiv created 2015/09/28 · arxiv updated 2015/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a (2p,q)-torus knot and M_n is a 3-manifold obtained by 1/n-Dehn surgery along K. We consider a polynomial whose zeros are the inverses of the Reideimeister torsion of M_n for SL(2;C)-irreducible representations. Johnson gave a formula for the case of the (2,3)-torus knot under some modification and normalization. We generalize this formula by using Tchebychev polynomials.

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