2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63720Motivated 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-infinity algebras have an interpretation as totally ramified extensions of discrete valuation rings. All A-infinity algebras are supposed to be unital and we give a detailed analysis of unital structures which is of independent interest.Slightly expanded version. Minor inaccuracies and misprints correctedQuantum AlgebraCommutative AlgebraAlgebraic Topology16E45, 14J10, 13F25, 13N15, 11S15text