## Homology, Homotopy and Applications

### Hochschild cohomology and moduli spaces of strongly homotopy associative algebras

A. Lazarev

#### Abstract

Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of invertible power series acting on a certain space. The Hochschild cohomology rings of resulting $A_\infty$-algebras have an interpretation as totally ramified extensions of discrete valuation rings. All $A_\infty$-algebras are supposed to be unital and we give a detailed analysis of unital structures which is of independent interest.

#### Article information

Source
Homology Homotopy Appl., Volume 5, Number 1 (2003), 73-100.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139839928

Mathematical Reviews number (MathSciNet)
MR1989615

Zentralblatt MATH identifier
1032.16008

Subjects
Primary: 55P15: Classification of homotopy type
Secondary: 55Q10: Stable homotopy groups

#### Citation

Lazarev, A. Hochschild cohomology and moduli spaces of strongly homotopy associative algebras. Homology Homotopy Appl. 5 (2003), no. 1, 73--100. https://projecteuclid.org/euclid.hha/1139839928