Maurer-Cartan elements in the Lie models of finite simplicial complexes
Algebraic Topology
2018-01-08 v2
Abstract
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
Cite
@article{arxiv.1606.08794,
title = {Maurer-Cartan elements in the Lie models of finite simplicial complexes},
author = {Urtzi Buijs and Yves Félix and Aniceto Murillo and Daniel Tanré},
journal= {arXiv preprint arXiv:1606.08794},
year = {2018}
}