On the Heegaard Floer homology of branched double-covers

Peter Ozsváth; Zoltán Szabó

doi:10.1016/j.aim.2004.05.008

On the Heegaard Floer homology of branched double-covers

Mathematics

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Abstract

Let L ⊂ S³ be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S³, branched along L. When L is an alternating link, HF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E² term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).

Original language	English (US)
Pages (from-to)	1-33
Number of pages	33
Journal	Advances in Mathematics
Volume	194
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2004.05.008
State	Published - Jun 20 2005

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Alternating links
Branched double-covers
Heegaard Floer homology
Khovanov's homology

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10.1016/j.aim.2004.05.008

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title = "On the Heegaard Floer homology of branched double-covers",

abstract = "Let L ⊂ S3 be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S3, branched along L. When L is an alternating link, HF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).",

keywords = "Alternating links, Branched double-covers, Heegaard Floer homology, Khovanov's homology",

author = "Peter Ozsv{\'a}th and Zolt{\'a}n Szab{\'o}",

note = "Funding Information: ∗Corresponding author. School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. E-mail addresses: [email protected] (P. Ozsv{\'a}th), [email protected] (Z. Szab{\'o}). 1Supported by NSF grant number DMS 0234311 and a Sloan Research Fellowship. 2Supported by NSF grant number DMS 0107792 and a Packard Fellowship.",

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T1 - On the Heegaard Floer homology of branched double-covers

AU - Ozsváth, Peter

AU - Szabó, Zoltán

N1 - Funding Information: ∗Corresponding author. School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. E-mail addresses: [email protected] (P. Ozsváth), [email protected] (Z. Szabó). 1Supported by NSF grant number DMS 0234311 and a Sloan Research Fellowship. 2Supported by NSF grant number DMS 0107792 and a Packard Fellowship.

PY - 2005/6/20

Y1 - 2005/6/20

N2 - Let L ⊂ S3 be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S3, branched along L. When L is an alternating link, HF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).

AB - Let L ⊂ S3 be a link. We study the Heegaard Floer homology of the branched double-cover ∑(L) of S3, branched along L. When L is an alternating link, HF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E2 term is a suitable variant of Khovanov's homology for the link L, converging to the Heegaard Floer homology of ∑(L).

KW - Alternating links

KW - Branched double-covers

KW - Heegaard Floer homology

KW - Khovanov's homology

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DO - 10.1016/j.aim.2004.05.008

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JO - Advances in Mathematics

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On the Heegaard Floer homology of branched double-covers

Abstract

All Science Journal Classification (ASJC) codes

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