A note on changemaker lattices and Alexander polynomials of lens space\n knots

2020/07/21 by Jacob Caudell, Caudell, Jacob
Computer Science · Materials Science · Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2007.11039

openalex publication_date 2020/07/21 · openalex created_date 2022/09/16 · openalex updated_date 2026/07/28

Abstract

We give an alternative proof of a recent theorem of Tange using the\ntechnology of changemaker lattices. Specifically, for K\⊂ S³ a\nnon-trivial knot with a lens space surgery, we give constraints on the\nAlexander polynomial of K and the lens space surgery when the coefficient of\nT^g(K)-2 in \Δ_K(T) is non-zero.\n

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