Dehn surgeries and rational homology balls

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 Donaldon's theorem, we classify which integral surgeries along torus knots of the form $T_{kq\pm 1,q}$ bound rational homology balls.

32 pages, many figures. Several minor improvements and corrections. Comments are welcome!

References in corpus (7)

• On the Floer homology of plumbed three-manifolds
• Heegaard Floer homology and alternating knots
• Lens spaces, rational balls and the ribbon conjecture
• Heegaard Floer homology and rational cuspidal curves
• Lens space surgeries and a conjecture of Goda and Teragaito
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Cited by in corpus (4)

• A survey of the homology cobordism group
• Using rational homology circles to construct rational homology balls
• Rational cobordisms and integral homology
• Embedding 3-manifolds in spin 4-manifolds