On the construction of A-infinity structures

Johannes Huebschmann (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We relate a construction of Kadeishvili establishing an A-infinity-structure on the homology of a differential graded algebra or more generally of an A-infinity algebra with certain constructions of Chen and Gugenheim. Thereafter we establish the links of these constructions with subsequent developments.

Mots clés: Ainfty-algebra; Cinftyalgebra; Linftyalgebra; twisting cochain; iterated integral; homological perturbation; minimality theorem; minimal model; perturbation lemma; (co)algebra perturbation lemma; Lie algebra perturbation lemma; differential graded Lie (co)algebra

Domaines: Topologie algébrique [math.AT]; Géométrie algébrique [math.AG]

Johannes Huebschmann. On the construction of A-infinity structures. Georgian J. Math., 2010, 17, pp.161-202. ⟨10.1515/GMJ.2010.004⟩. ⟨hal-00799535⟩