Algebraic & Geometric Topology

Dehn surgeries and rational homology balls

Paolo Aceto and Marco Golla

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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.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 487-527.

Dates
Received: 14 April 2016
Revised: 8 June 2016
Accepted: 15 June 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841319

Digital Object Identifier
doi:10.2140/agt.2017.17.487

Mathematical Reviews number (MathSciNet)
MR3604383

Zentralblatt MATH identifier
1359.57009

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57R58: Floer homology

Keywords
Dehn surgery rational balls Heegaard Floer correction terms torus knots lattices

Citation

Aceto, Paolo; Golla, Marco. Dehn surgeries and rational homology balls. Algebr. Geom. Topol. 17 (2017), no. 1, 487--527. doi:10.2140/agt.2017.17.487. https://projecteuclid.org/euclid.agt/1510841319


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