Enhanced $A$-infinity obstruction theory

Abstract

We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of truncated minimal A-infinity algebra structures. We also consider the Bousfield-Kan spectral sequence for the moduli space of A-infinity algebras. We compute up to the second page, terms and differentials, of these spectral sequences in terms of Hochschild cohomology.

42 pages, color figures

References in corpus (4)

• Homotopy theory of non-symmetric operads
• Homotopy unital A_infinity-algebras
• Fibers of partial totalizations of a pointed cosimplicial space
• Cylinders for non-symmetric DG-operads via homological perturbation theory

Cited by in corpus (2)

• The Donovan--Wemyss Conjecture via the Derived Auslander--Iyama Correspondence
• Enhanced finite triangulated categories