Dehn surgeries and negative-definite four-manifolds

2011/08/24 by Brendan Owens, Owens, Brendan, Sašo Strle +2 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.1108.4869

16 pages, 5 figures

arxiv created 2011/08/24 · openalex publication_date 2011/08/24 · arxiv updated 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a knot K in the three-sphere, we address the question: which Dehn surgeries on K bound negative-definite four-manifolds? We show that the answer depends on a number m(K), which is a smooth concordance invariant. We study the properties of this invariant, and compute it for torus knots.

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