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

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Cited by in corpus (4)

• From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron
• Trivalent vertices and bordered knot Floer homology in the standard basis
• Compatibility in Ozsvath-Szabo's bordered HFK via higher representations
• Strands algebras and the affine highest weight property for equivariant hypertoric categories