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GENERATORS, RELATIONS, AND HOMOLOGY FOR OZSVÁTH–SZABÓ’S KAUFFMAN-STATES ALGEBRAS

Part of: Homological methods Differential topology Low-dimensional topology

Published online by Cambridge University Press:  17 April 2020

ANDREW MANION Open the ORCID record for ANDREW MANION [Opens in a new window] ,
MARCO MARENGON  and
MICHAEL WILLIS
ANDREW MANION
Affiliation:
Department of Mathematics, USC, 3620 S. Vermont Ave., Los Angeles, CA 90089, USA email amanion@usc.edu
MARCO MARENGON
Affiliation:
Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, USA email marengon@math.ucla.edu
MICHAEL WILLIS
Affiliation:
Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, USA email mike.willis@math.ucla.edu
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Abstract

We give a generators-and-relations description of differential graded algebras recently introduced by Ozsváth and Szabó for the computation of knot Floer homology. We also compute the homology of these algebras and determine when they are formal.

MSC classification

Primary: 57R58: Floer homology
Secondary: 16E45: Differential graded algebras and applications 57M27: Invariants of knots and 3-manifolds 57R56: Topological quantum field theories
Type
Article
Information
Nagoya Mathematical Journal , Volume 244 , December 2021 , pp. 60 - 118
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Copyright
© 2020 Foundation Nagoya Mathematical Journal

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Footnotes

A.M. was supported by an NSF MSPRF fellowship, grant number DMS-1502686. M.M. was supported by the NSF FRG grant DMS-1563615. M.W. was supported by the NSF FRG grant DMS-1563615.

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