Article

Selecta Mathematica

, Volume 18, Issue 4, pp 839-854

First online:

Dehn surgeries and negative-definite four-manifolds

  • Brendan OwensAffiliated withSchool of Mathematics and Statistics, University of Glasgow Email author 
  • , Sašo StrleAffiliated withFaculty of Mathematics and Physics, University of Ljubljana

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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.

Keywords

Dehn surgery Smooth negative-definite four-manifold Torus knot Concordance

Mathematics Subject Classification (2000)

57M27 57Q60