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

Manion, Andrew¹ ; Marengon, Marco² ; Willis, Michael²

¹Department of Mathematics, University of Southern California, Los Angeles, CA, United States
²Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, United States

Algebraic and Geometric Topology, Tome 20 (2020) no. 7, pp. 3607-3706

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.3607

Classification : 57M25, 57M27, 57R56, 57R58
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

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