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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

    Brendan Owens

  2. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000, Ljubljana, Slovenia

    Sašo Strle

Authors
  1. Brendan Owens
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  2. Sašo Strle
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Corresponding author

Correspondence to Brendan Owens.

Additional information

Dedicated to José Maria Montesinos on the occasion of his 65th birthday.

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.

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Owens, B., Strle, S. Dehn surgeries and negative-definite four-manifolds. Sel. Math. New Ser. 18, 839–854 (2012). https://doi.org/10.1007/s00029-012-0086-2

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