Diagonals and A-infinity Tensor Products

2020/09/11 by Lipshitz, Robert, Ozsváth, Peter, Thurston, Dylan
#FOS: Mathematics #Geometric Topology (math.GT) #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2009.05222

Abstract

Extending work of Saneblidze-Umble and others, we use diagonals for the associahedron and multiplihedron to define tensor products of A-infinity algebras, modules, algebra homomorphisms, and module morphisms, as well as to define a bimodule analogue of twisted complexes (type DD structures, in the language of bordered Heegaard Floer homology) and their one- and two-sided tensor products. We then give analogous definitions for 1-parameter deformations of A-infinity algebras; this involves another collection of complexes. These constructions are relevant to bordered Heegaard Floer homology.

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