2017/08/31 by Teruhisa Kadokami, Kadokami, Teruhisa, Noriko Maruyama +3
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1708.09802
openalex publication_date 2017/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a knot K in a homology 3-sphere Σ, let M be the result of 2/q-surgery on K, and let X be the universal abelian covering of M. Our first theorem is that if the first homology of X is finite cyclic and M is a Seifert fibered space with N≥ 3 singular fibers, then N≥ 4 if and only if the first homology of the universal abelian covering of X is infinite. Our second theorem is that under an appropriate assumption on the Alexander polynomial of K, if M is a Seifert fibered space, then q=± 1 (i.e. integral surgery).