Maurer-Cartan Elements in the Lie Models of Finite Simplicial Complexes
Printed: Sep 2017
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.
complete differential graded Lie algebra, Maurer-Cartan element, rational homotopy theory
16E45 - Differential graded algebras and applications