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

Abstract

We define new differential graded algebras A(n,k,S) in the framework of Lipshitz-Ozsváth-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-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-Szabó's gradings on B(n,k,S) arise naturally from the general framework of group-valued gradings on strands algebras.

76 pages; 24 figures