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Strands algebras and
Ozsváth and Szabó's Kauffman-states functor
Andrew Manion, Marco Marengon and Michael Willis |
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Algebraic & Geometric Topology 20 (2020) 3607–3706
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Abstract |
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We define new differential graded algebras in the framework of Lipshitz, Ozsváth and Thurston’s and Zarev’s strands algebras from bordered Floer homology. The algebras are meant to be strands models for Ozsváth and Szabó’s algebras ; indeed, we exhibit a quasi-isomorphism from to . We also show how Ozsváth and Szabó’s gradings on arise naturally from the general framework of group-valued gradings on strands algebras. |
Keywords
strands algebras, Floer homology, bordered Floer homology,
sutured manifolds, bordered sutured Floer homology,
A-infinity algebras, Kauffman states, knot Floer homology,
tangle Floer homology, bordered knot Floer homology
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R56
Secondary: 57R58
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References |
Publication
Received: 7 September 2019
Revised: 8 March 2020
Accepted: 26 March 2020
Published: 29 December 2020
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Authors |
| Andrew Manion | |
| Department of Mathematics University of Southern California Los Angeles, CA United States |
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| Marco Marengon | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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| Michael Willis | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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