2024/05/20 by Antony T. H. Fung, Fung, Antony T. H.
Mathematics · #57K10 #57N70 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2405.11736
openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Cyclic Surgery Theorem and Moser's work on surgeries on torus knots imply that for any non-trivial knot in S3, there are at most two integer surgeries that produce a lens space. This paper investigates how many positive integer surgeries on a given knot in S3 can produce a manifold rational homology cobordant to a lens space. Tools include Greene and McCoy's work on changemaker lattices which come from Heegaard Floer d-invariants, and Aceto-Celoria-Park's work on rational cobordisms and integral homology which is based on Lisca's work on lens spaces.