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.
Homology, Homotopy and Applications, Vol. 13 (2011), No. 2, pp.175-195.
Available as: dvi dvi.gz ps ps.gz pdf