Strands algebras and Ozsv\'ath-Szab\'o's Kauffman-states functor

Andrew Manion; Marco Marengon; Michael Willis

doi:10.2140/agt.2020.20.3607

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arXiv · 1903.05655

Strands algebras and Ozsv\'ath-Szab\'o's Kauffman-states functor

Andrew Manion·Marco Marengon·Michael Willis

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Abstract

We define new differential graded algebras A(n,k,S) in the framework of Lipshitz-Ozsv\'ath-Thurston's and Zarev's strands algebras from bordered Floer homology. The algebras A(n,k,S) are meant to be strands models for Ozsv\'ath-Szab\'o'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 Ozsv\'ath-Szab\'o's gradings on B(n,k,S) arise naturally from the general framework of group-valued gradings on strands algebras.

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Andrew Manion, Marco Marengon, Michael Willis. 2019-03-13. Strands algebras and Ozsv\'ath-Szab\'o's Kauffman-states functor. https://doi.org/10.2140/agt.2020.20.3607

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