A combinatorial description of knot Floer homology

Ciprian Manolescu; Peter Ozsváth; Sucharit Sarkar

doi:10.4007/annals.2009.169.633

A combinatorial description of knot Floer homology

Ciprian Manolescu, Peter Ozsváth, Sucharit Sarkar

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

111 Scopus citations

Abstract

Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.

Original language	English (US)
Pages (from-to)	633-660
Number of pages	28
Journal	Annals of Mathematics
Volume	169
Issue number	2
DOIs	https://doi.org/10.4007/annals.2009.169.633
State	Published - 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.4007/annals.2009.169.633

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title = "A combinatorial description of knot Floer homology",

abstract = "Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.",

author = "Ciprian Manolescu and Peter Ozsv{\'a}th and Sucharit Sarkar",

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AU - Manolescu, Ciprian

AU - Ozsváth, Peter

AU - Sarkar, Sucharit

PY - 2009

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AB - Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.

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M3 - Article

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EP - 660

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

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A combinatorial description of knot Floer homology

Abstract

All Science Journal Classification (ASJC) codes

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