Diagonals and A-infinity Tensor Products

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.

arXiv comment169 pages, 49 figures. V2: add a citation. v3: Minor edits

References in corpus (10)

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Cited by in corpus (2)

• Tautological classes and symmetry in Khovanov-Rozansky homology
• A bordered HF- algebra for the torus