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arXiv · 1606.08794

Maurer-Cartan elements in the Lie models of finite simplicial complexes

Urtzi Buijs·Yves Félix·Aniceto Murillo·Daniel Tanré
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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.

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Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré. 2016-06-28. Maurer-Cartan elements in the Lie models of finite simplicial complexes. https://arxiv.org/abs/1606.08794

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