1. CMB Online first
||Maurer-Cartan elements in the Lie models of finite simplicial complexes|
In a previous work, we have associated a complete differential
graded Lie algebra
to any finite simplicial complex in a functorial way.
Similarly, we have also a realization functor from the category
of complete differential graded Lie algebras
to the category of simplicial sets.
We have already interpreted the homology of a Lie algebra
in terms of homotopy groups of its realization.
In this paper, we begin a dictionary between models
and simplicial complexes by establishing a correspondence
between the Deligne groupoid of the model and the connected components
of the finite simplicial complex.
Keywords:complete differential graded Lie algebra, Maurer-Cartan element, rational homotopy theory
2. CMB 2011 (vol 54 pp. 472)
||A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps|
We study infinitesimal deformations of holomorphic maps of
compact, complex, KÃ¤hler manifolds. In particular, we describe a
generalization of Bloch's semiregularity map that annihilates
obstructions to deform holomorphic maps with fixed codomain.
Keywords:semiregularity map, obstruction theory, functors of Artin rings, differential graded Lie algebras
Categories:13D10, 14D15, 14B10