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Mathematics > Geometric Topology

Title: A-infinity algebras, strand algebras, and contact categories

Abstract: In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered Floer theory. Being isomorphic to the homology of a differential graded algebra, this contact category algebra has an A-infinity structure. In this paper we investigate such A-infinity structures in detail. We give explicit constructions of such A-infinity structures, and establish some of their properties, including conditions for the nonvanishing of A-infinity operations. Along the way we develop several related notions, including a detailed consideration of tensor products of strand diagrams.
Comments: 83 pages, 23 figures, 6 tables
Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT); Symplectic Geometry (math.SG)
MSC classes: 57R17 (Primary), 57R58, 16E40, 16E45
Cite as: arXiv:1803.06455 [math.GT]
  (or arXiv:1803.06455v1 [math.GT] for this version)

Submission history

From: Daniel Mathews [view email]
[v1] Sat, 17 Mar 2018 04:09:27 GMT (98kb)