(83 pages) – on the arXiv — published in Algebraic & Geometric Topology.
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.
- pdf (1.06 Mb)
agt-v21-n3-p02-s
A-infinity algebras, strand algebras, and contact categories