Surgery obstructions and Heegaard Floer homology

Hom, Jennifer; Karakurt, Çağrı; Lidman, Tye

doi:10.2140/gt.2016.20.2219

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Surgery obstructions and Heegaard Floer homology

Jennifer Hom, Çağrı Karakurt and Tye Lidman

Geometry & Topology 20 (2016) 2219–2251

DOI: 10.2140/gt.2016.20.2219

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

Volume 20, issue 4 (2016)