Combinatorial Heegaard Floer homology and nice Heegaard diagrams

Peter Ozsváth; András I. Stipsicz; Zoltán Szabó

doi:10.1016/j.aim.2012.04.008

Combinatorial Heegaard Floer homology and nice Heegaard diagrams

Peter Ozsváth
, András I. Stipsicz
, Zoltán Szabó

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider a stabilized version of HF̂ of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a topological proof of its invariance properties.

Original language	English (US)
Pages (from-to)	102-171
Number of pages	70
Journal	Advances in Mathematics
Volume	231
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2012.04.008
State	Published - Sep 10 2012

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Floer homology
Heegaard decompositions
Pair-of-pants decompositions

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10.1016/j.aim.2012.04.008

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title = "Combinatorial Heegaard Floer homology and nice Heegaard diagrams",

abstract = "We consider a stabilized version of H{\^F} of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a topological proof of its invariance properties.",

keywords = "Floer homology, Heegaard decompositions, Pair-of-pants decompositions",

author = "Peter Ozsv{\'a}th and Stipsicz, \{Andr{\'a}s I.\} and Zolt{\'a}n Szab{\'o}",

note = "Funding Information: PSO was supported by NSF grant number DMS-0804121 . AS was supported by OTKA NK81203 . ZSz was supported by NSF grant numbers DMS-0704053 , DMS-1006006 . We would like to thank the Mathematical Sciences Research Institute, Berkeley for providing a productive research environment. We would like to thank Jean-Mathieu Magot and an anonymous referee for many useful comments and suggestions for improving the presentation of our results. ",

year = "2012",

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doi = "10.1016/j.aim.2012.04.008",

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journal = "Advances in Mathematics",

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T1 - Combinatorial Heegaard Floer homology and nice Heegaard diagrams

AU - Ozsváth, Peter

AU - Stipsicz, András I.

AU - Szabó, Zoltán

N1 - Funding Information: PSO was supported by NSF grant number DMS-0804121 . AS was supported by OTKA NK81203 . ZSz was supported by NSF grant numbers DMS-0704053 , DMS-1006006 . We would like to thank the Mathematical Sciences Research Institute, Berkeley for providing a productive research environment. We would like to thank Jean-Mathieu Magot and an anonymous referee for many useful comments and suggestions for improving the presentation of our results.

PY - 2012/9/10

Y1 - 2012/9/10

N2 - We consider a stabilized version of HF̂ of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a topological proof of its invariance properties.

AB - We consider a stabilized version of HF̂ of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a topological proof of its invariance properties.

KW - Floer homology

KW - Heegaard decompositions

KW - Pair-of-pants decompositions

UR - https://www.scopus.com/pages/publications/84861632697

UR - https://www.scopus.com/pages/publications/84861632697#tab=citedBy

U2 - 10.1016/j.aim.2012.04.008

DO - 10.1016/j.aim.2012.04.008

M3 - Article

AN - SCOPUS:84861632697

SN - 0001-8708

VL - 231

SP - 102

EP - 171

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Combinatorial Heegaard Floer homology and nice Heegaard diagrams

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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