#### Volume 20, issue 4 (2016)

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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
##### 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