L-infinity maps and twistings

摘要

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