Finite knot surgeries and Heegaard Floer homology

Details Finite knot surgeries and Heegaard Floer homology Finite knot surgeries and Heegaard Floer homology

2012-01-19

arxiv.org/abs/1201.4187v1

Mathematics

Geometric Topology

26 pages, 1 figure

Scientific paper

It is well known that any 3-manifold can be obtained by Dehn surgery on a link but not which ones can be obtained from a knot or which knots can produce them. We investigate these two questions for elliptic Seifert fibered spaces (other than lens spaces) using the Heegaard Floer correction terms associated to a 3-manifold Y and its torsion Spin^c structures. If H_1(Y) is finite and small, the correction terms completely identify the manifolds which can be realized as knot surgeries and the knots which realize them; even when H_1(Y) is larger (but still finite), the invariants help identify the manifolds and place restrictions on the knots.

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