Dehn surgeries and negative-definite four-manifolds Authors Brendan Owens School of Mathematics and Statistics University of Glasgow Sašo Strle Faculty of Mathematics and Physics University of Ljubljana Article

First Online: 28 January 2012 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
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 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.

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