Surgery obstructions and Heegaard Floer homology

Hom, Jennifer¹ ; Karakurt, Çağrı² ; Lidman, Tye³

¹ School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States
² Department of Mathematics, Boğaziçi University, 34342 Bebek, Istanbul, Turkey
³ Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States

Geometry & topology, Tome 20 (2016) no. 4, pp. 2219-2251.

Résumé

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.

Détail

DOI : 10.2140/gt.2016.20.2219

Classification : 57M27, 57R58, 57R65
Keywords: Dehn surgery, $3$–manifold, Floer homology

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