On the moduli space of A-infinity structures

TL;DR

This paper investigates the structure of the moduli space of A-infinity structures on topological spaces and modules, revealing their relationship with Hochschild cohomology through homotopy fiber sequences.

Contribution

It establishes a homotopy fiber sequence linking the moduli spaces of A-infinity structures to Hochschild cohomology spaces, advancing understanding of their topological and algebraic properties.

Findings

Moduli space of A-infinity structures fits into a homotopy fiber sequence.

Homotopy fiber sequence relates these moduli spaces to Hochschild cohomology.

Provides new insights into the topological and algebraic structure of A-infinity moduli spaces.

Abstract

We study the moduli space of A-infinity structures on a topological space as well as the moduli space of A-infinity-ring structures on a fixed module spectrum. In each case we show that the moduli space sits in a homotopy fiber sequence in which the other terms are representing spaces for Hochschild cohomology.