The third term in lens surgery polynomials

2020/05/18 by Motoo Tange, Tange, Motoo
Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2005.09004

openalex publication_date 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well-known that the second coefficient of the Alexander polynomial of any lens space knot in S³ is -1. We show that the non-zero third coefficient condition of the Alexander polynomial of a lens space knot K in S³ confines the surgery to the one realized by the (2,2g+1)-torus knot, where g is the genus of K. In particular, such a lens surgery polynomial coincides with Δ_T(2,2g+1)(t).

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