Homology, Homotopy and Applications
Volume 13 (2011)
L-infinity maps and twistings
Pages: 175 – 195
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.
differential graded Lie algebra; Maurer-Cartan element; $A_\infty$ algebra; graph homology; Morita equivalence
2010 Mathematics Subject Classification
16E45, 18D50, 57T30, 81T18