The mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in $S^3$
| Autor: | Fyodor Gainullin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mapping cone (topology)
010102 general mathematics Geometric Topology (math.GT) 01 natural sciences Mathematics::Geometric Topology Heegaard Floer homology Dehn surgery Combinatorics Mathematics - Geometric Topology Floer homology 57M27 0103 physical sciences 57M25 FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Algebr. Geom. Topol. 17, no. 4 (2017), 1917-1951 |
| ISSN: | 1917-1951 |
| Popis: | 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. 28 pages, 3 figures; accepted for publication in AGT, incorporates corrections resulting from the referee's comments |
| Databáze: | OpenAIRE |
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