Heegaard Floer groups of Dehn surgeries

Stanislav Jabuka

doi:10.1112/jlms/jdv038

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arXiv · 1409.6236

Heegaard Floer groups of Dehn surgeries

Stanislav Jabuka

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Abstract

We use an algorithm by Ozsvath and Szabo to find closed formulae for the ranks of the hat version of the Heegaard Floer homology groups for non-zero Dehn surgeries on knots in the 3-sphere. As applications we provide new bounds on the number of distinct ranks of the Heegaard Floer groups a Dehn surgery can have. These in turn give a new lower bound on the rational Dehn surgery genus of a rational homology 3-sphere. We also provide novel obstructions for a knot to be a potential counterexample to the Cabling Conjecture.

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BibTeX RIS

Stanislav Jabuka. 2014-09-22. Heegaard Floer groups of Dehn surgeries. https://doi.org/10.1112/jlms%2Fjdv038

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