Null-homologous twisting and the algebraic genus

2019/08/12 by Duncan McCoy, McCoy, Duncan
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1908.04043

openalex publication_date 2019/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The algebraic genus of a knot is an invariant that arises when one considers upper bounds for the topological slice genus coming from Freedman's theorem that Alexander polynomial one knots are topologically slice. This paper develops null-homologous twisting operations as a tool for studying the algebraic genus and, consequently, for bounding the topological slice genus above. As applications we give new upper bounds on the algebraic genera of torus knots and satellite knots.

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