Abstract
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.
Citation
Joseph Chuang. Andrey Lazarev. "L-infinity maps and twistings." Homology Homotopy Appl. 13 (2) 175 - 195, 2011.
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