Geometry & Topology

Surgery obstructions and Heegaard Floer homology

Jennifer Hom, Çağrı Karakurt, and Tye Lidman

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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.

Article information

Geom. Topol., Volume 20, Number 4 (2016), 2219-2251.

Received: 7 January 2015
Revised: 12 August 2015
Accepted: 10 November 2015
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology 57R65: Surgery and handlebodies

Dehn surgery $3$–manifold Floer homology


Hom, Jennifer; Karakurt, Çağrı; Lidman, Tye. Surgery obstructions and Heegaard Floer homology. Geom. Topol. 20 (2016), no. 4, 2219--2251. doi:10.2140/gt.2016.20.2219.

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