, Volume 18, Issue 4, pp 839-854
Date: 28 Jan 2012

Dehn surgeries and negative-definite four-manifolds

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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.

B. Owens was supported in part by NSF grant DMS-0604876 and by the EPSRC. S. Strle was supported in part by the ARRS of the Republic of Slovenia research programme No. P1-0292-0101. We also acknowledge support from the ESF through the ITGP programme.
Dedicated to José Maria Montesinos on the occasion of his 65th birthday.