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L -infinity maps and twistings

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<mark>Journal publication date</mark>2011
<mark>Journal</mark>Homology, Homotopy and Applications
Issue number2
Number of pages21
Pages (from-to)175-195
<mark>Original language</mark>English


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.