On the Alexander polynomial and the signature invariant of two-bridge knots

2017/12/13 by Wenzhao Chen, Chen, Wenzhao · 1 citation
Mathematics · Medicine · #Bone health and treatments #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.1712.04993

minor errors corrected

arxiv created 2018/01/10 · arxiv updated 2018/01/12

Abstract

Fox conjectured the Alexander polynomial of an alternating knot is trapezoidal, i.e. the coefficients first increase, then stabilize and finally decrease in a symmetric way. Recently, Hirasawa and Murasugi further conjectured a relation between the number of the stable coefficients in the Alexander polynomial and the signature invariant. In this paper we prove the Hirasawa-Murasugi conjecture for two-bridge knots.

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• Knot Floer homology of satellite knots with (1,1)-patterns

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