Khovanov-Seidel quiver algebras and bordered Floer homology

Denis Auroux; J. Elisenda Grigsby; Stephan M. Wehrli

doi:10.1007/s00029-012-0106-2

Khovanov-Seidel quiver algebras and bordered Floer homology

Denis Auroux, J. Elisenda Grigsby, Stephan M. Wehrli

Department of Mathematics

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

7 Scopus citations

Abstract

We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associated to the double-branched cover of a braid and show that its associated graded bimodule is equivalent to a similar bimodule defined by Khovanov and Seidel.

Original language	English (US)
Pages (from-to)	1-55
Number of pages	55
Journal	Selecta Mathematica, New Series
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s00029-012-0106-2
State	Published - Jan 2014

Keywords

Braids
Heegaard Floer homology
Khovanov homology

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

Access to Document

10.1007/s00029-012-0106-2

Cite this

@article{cc9a4639ab8548338f5d5645db5b09da,

title = "Khovanov-Seidel quiver algebras and bordered Floer homology",

abstract = "We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associated to the double-branched cover of a braid and show that its associated graded bimodule is equivalent to a similar bimodule defined by Khovanov and Seidel.",

keywords = "Braids, Heegaard Floer homology, Khovanov homology",

author = "Denis Auroux and Grigsby, {J. Elisenda} and Wehrli, {Stephan M.}",

note = "Funding Information: DA was partially supported by NSF grant DMS-1007177. JEG was partially supported by a Viterbi-endowed MSRI postdoctoral fellowship and NSF grant number DMS-0905848. SMW was partially supported by an MSRI postdoctoral fellowship.",

year = "2014",

month = jan,

doi = "10.1007/s00029-012-0106-2",

language = "English (US)",

volume = "20",

pages = "1--55",

journal = "Selecta Mathematica, New Series",

issn = "1022-1824",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - Khovanov-Seidel quiver algebras and bordered Floer homology

AU - Auroux, Denis

AU - Grigsby, J. Elisenda

AU - Wehrli, Stephan M.

N1 - Funding Information: DA was partially supported by NSF grant DMS-1007177. JEG was partially supported by a Viterbi-endowed MSRI postdoctoral fellowship and NSF grant number DMS-0905848. SMW was partially supported by an MSRI postdoctoral fellowship.

PY - 2014/1

Y1 - 2014/1

N2 - We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associated to the double-branched cover of a braid and show that its associated graded bimodule is equivalent to a similar bimodule defined by Khovanov and Seidel.

AB - We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associated to the double-branched cover of a braid and show that its associated graded bimodule is equivalent to a similar bimodule defined by Khovanov and Seidel.

KW - Braids

KW - Heegaard Floer homology

KW - Khovanov homology

UR - http://www.scopus.com/inward/record.url?scp=84891658661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891658661&partnerID=8YFLogxK

U2 - 10.1007/s00029-012-0106-2

DO - 10.1007/s00029-012-0106-2

M3 - Article

AN - SCOPUS:84891658661

SN - 1022-1824

VL - 20

SP - 1

EP - 55

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 1

ER -

Khovanov-Seidel quiver algebras and bordered Floer homology

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this