Surgery obstructions and Heegaard Floer homology

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 give an obstruction to a homology sphere being surgery on a knot coming from Heegaard Floer homology. This is used to construct infinitely many small Seifert fibered examples.

References in corpus (2)

• Calculating Heegaard-Floer Homology by Counting Lattice Points in Tetrahedra
• Finite knot surgeries and Heegaard Floer homology

Cited by in corpus (6)

• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• A survey of the homology cobordism group
• Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology
• Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
• Ozsvath-Szabo $d$-invariants of almost simple linear graphs
• Surgery obstructions and character varieties