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arXiv · 1411.1275

Mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in $S^3$

Fyodor Gainullin
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Abstract

We write down an explicit formula for the $+$ version of the Heegaard Floer homology (as an absolutely graded vector space over an arbitrary field) of the results of Dehn surgery on a knot $K$ in $S^3$ in terms of homological data derived from $CFK^{\infty}(K)$. This allows us to prove some results about Dehn surgery on knots in $S^3$. In particular, we show that for a fixed manifold there are only finitely many alternating knots that can produce it by surgery. This is an improvement on a recent result by Lackenby and Purcell. We also derive a lower bound on the genus of knots depending on the manifold they give by surgery. Some new restrictions on Seifert fibred surgery are also presented.

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BibTeXRIS

Fyodor Gainullin. 2017-08-05. Mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in $S^3$. https://doi.org/10.2140/agt.2017.17.1917

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