Volume 17, issue 1 (2017)

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Dehn surgeries and rational homology balls

Paolo Aceto and Marco Golla

Algebraic & Geometric Topology 17 (2017) 487–527
Abstract

We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsváth and Szabó’s correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on positive torus knots. Finally, combining these results with a lattice-theoretic obstruction based on Donaldson’s theorem, we classify which integral surgeries along torus knots of the form ${T}_{kq±1,q}$ bound rational homology balls.

Keywords
Dehn surgery, rational balls, Heegaard Floer correction terms, torus knots, lattices
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25, 57R58
Publication
Revised: 8 June 2016
Accepted: 15 June 2016
Published: 26 January 2017
Authors
 Paolo Aceto Alfréd Rényi Institute of Mathematics 13–15 Reáltanoda u Budapest 1053 Hungary http://www.renyi.hu/~paoloace/ Marco Golla Department of Mathematics Uppsala University Box 480 SE-751 06 Uppsala Sweden http://www2.math.uu.se/~margo137/