L -infinity maps and twistings

Chuang, Joseph and Lazarev, Andrey (2011) L -infinity maps and twistings. Homology, Homotopy and Applications, 13 (2). pp. 175-195. ISSN 1532-0073

Abstract

We give a construction of an L∞ map from any L∞ algebra into its truncated Chevalley-Eilenberg complex as well as its cyclic and A∞ analogues. This map fits with the inclusion into the full Chevalley-Eilenberg complex (or its respective analogues) to form a homotopy fiber sequence of L∞ algebras. Applications to deformation theory and graph homology are given. We employ the machinery of Maurer-Cartan functors in L∞ and A∞ algebras and associated twistings which should be of independent interest.