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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Surgery obstructions and Heegaard Floer homology

Jennifer Hom, Çağrı Karakurt and Tye Lidman

Geometry & Topology 20 (2016) 2219–2251
Abstract

Using Taubes’ periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We use Heegaard Floer homology to give an obstruction to a homology sphere being surgery on a knot, and then use this obstruction to construct infinitely many small Seifert fibered examples.

Keywords
Dehn surgery, $3$–manifold, Floer homology
Mathematical Subject Classification 2010
Primary: 57M27, 57R58, 57R65
References
Publication
Received: 7 January 2015
Revised: 12 August 2015
Accepted: 10 November 2015
Published: 15 September 2016
Proposed: Ronald Stern
Seconded: Ciprian Manolescu, Peter S. Ozsváth
Authors
Jennifer Hom
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332
United States
Çağrı Karakurt
Department of Mathematics
Boğaziçi University
34342 Bebek
Istanbul
Turkey
Tye Lidman
Department of Mathematics
North Carolina State University
Raleigh, NC 27695
United States