2014/09/17 by Tetsuya Abe, Abe, Tetsuya, In Dae Jong +5
Computer Science · Mathematics · #57M25 #57M27 #57R65 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1409.4851
openalex publication_date 2014/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that for any integer n there exist infinitely many different knots in S3 such that n-surgery on those knots yields the same 3-manifold. In particular, when |n|=1 homology spheres arise from these surgeries. This answers Problem 3.6(D) on the Kirby problem list. We construct two families of examples, the first by a method of twisting along an annulus and the second by a generalization of this procedure. The latter family also solves a stronger version of Problem 3.6(D), that for any integer n, there exist infinitely many mutually distinct knots such that 2-handle addition along each with framing n yields the same 4-manifold.