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2020 Strands algebras and Ozsváth and Szabó's Kauffman-states functor
Andrew Manion, Marco Marengon, Michael Willis
Algebr. Geom. Topol. 20(7): 3607-3706 (2020). 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 (n,k,𝒮); indeed, we exhibit a quasi-isomorphism from (n,k,𝒮) to 𝒜(n,k,𝒮). We also show how Ozsváth and Szabó’s gradings on (n,k,𝒮) arise naturally from the general framework of group-valued gradings on strands algebras.

Citation

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Andrew Manion. Marco Marengon. Michael Willis. "Strands algebras and Ozsváth and Szabó's Kauffman-states functor." Algebr. Geom. Topol. 20 (7) 3607 - 3706, 2020. https://doi.org/10.2140/agt.2020.20.3607

Information

Received: 7 September 2019; Revised: 8 March 2020; Accepted: 26 March 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194290
Digital Object Identifier: 10.2140/agt.2020.20.3607

Subjects:
Primary: 57M25, 57M27, 57R56
Secondary: 57R58

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 7 • 2020
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