Enhanced $A$-infinity obstruction theory

TL;DR

This paper extends spectral sequences to compute homotopy groups and obstructions for minimal A-infinity algebra structures, linking them to Hochschild cohomology, and explores their moduli spaces.

Contribution

It introduces an enhanced obstruction theory for A-infinity structures and computes spectral sequence terms using Hochschild cohomology.

Findings

Extended spectral sequence for A-infinity structures

Defined new obstructions for extending truncated structures

Computed spectral sequence pages and differentials

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.