Dehn surgeries and rational homology balls

Aceto, Paolo¹ ; Golla, Marco²

¹Alfréd Rényi Institute of Mathematics, 13–15 Reáltanoda u, Budapest, 1053, Hungary
²Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden

Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 487-527

Résumé

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.

Détail

DOI : 10.2140/agt.2017.17.487

Classification : 57M27, 57M25, 57R58
Keywords: Dehn surgery, rational balls, Heegaard Floer correction terms, torus knots, lattices

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