Selecta Mathematica

, Volume 18, Issue 4, pp 839–854

Dehn surgeries and negative-definite four-manifolds


DOI: 10.1007/s00029-012-0086-2

Cite this article as:
Owens, B. & Strle, S. Sel. Math. New Ser. (2012) 18: 839. doi:10.1007/s00029-012-0086-2


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.


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

Mathematics Subject Classification (2000)

57M27 57Q60 

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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