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L -infinity maps and twistings

Research output: Contribution to journalJournal article

Published

Journal publication date2011
JournalHomology, Homotopy and Applications
Journal number2
Volume13
Number of pages21
Pages175-195
Original languageEnglish

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.