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