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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 Tkq±1,q bound rational homology balls.

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Keywords
Dehn surgery, rational balls, Heegaard Floer correction terms, torus knots, lattices
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25, 57R58
References
Publication
Received: 14 April 2016
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/