Strands algebras and Ozsváth and Szabó’s Kauffman-states functor

Manion, Andrew; Marengon, Marco; Willis, Michael

doi:10.2140/agt.2020.20.3607

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Strands algebras and Ozsváth and Szabó's Kauffman-states functor

Andrew Manion, Marco Marengon and Michael Willis

Algebraic & Geometric Topology 20 (2020) 3607–3706

DOI: 10.2140/agt.2020.20.3607

Abstract

We define new differential graded algebras $𝒜 (n, k, 𝒮)$ in the framework of Lipshitz, Ozsváth and Thurston’s and Zarev’s strands algebras from bordered Floer homology. The algebras $𝒜 (n, k, 𝒮)$ are meant to be strands models for Ozsváth and Szabó’s algebras $ℬ (n, k, 𝒮)$ ; indeed, we exhibit a quasi-isomorphism from $ℬ (n, k, 𝒮)$ to $𝒜 (n, k, 𝒮)$ . We also show how Ozsváth and Szabó’s gradings on $ℬ (n, k, 𝒮)$ arise naturally from the general framework of group-valued gradings on strands algebras.

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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

Mathematical Subject Classification 2010

Primary: 57M25, 57M27, 57R56

Secondary: 57R58

References

Publication

Received: 7 September 2019

Revised: 8 March 2020

Accepted: 26 March 2020

Published: 29 December 2020

Authors

Andrew Manion
Department of Mathematics University of Southern California Los Angeles, CA United States

Marco Marengon
Department of Mathematics University of California, Los Angeles Los Angeles, CA United States

Michael Willis
Department of Mathematics University of California, Los Angeles Los Angeles, CA United States

Volume 20, issue 7 (2020)