Geodesic
Maurer–Cartan Elements in the Lie Models of Finite Simplicial Complexes
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 470-477

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DOI

In a previous work, we associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we also have a realization functor fromthe 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.
DOI : 10.4153/CMB-2017-003-7
Mots-clés : 55P62, 16E45, complete diÒerential graded Lie algebra, Maurer–Cartan elements, rational homotopy theory 
Buijs, Urtzi; Félix, Yves; Murillo, Aniceto; Tanré, Daniel. Maurer–Cartan Elements in the Lie Models of Finite Simplicial Complexes. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 470-477. doi: 10.4153/CMB-2017-003-7
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     title = {Maurer{\textendash}Cartan {Elements} in the {Lie} {Models} of {Finite} {Simplicial} {Complexes}},
     journal = {Canadian mathematical bulletin},
     pages = {470--477},
     year = {2017},
     volume = {60},
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     doi = {10.4153/CMB-2017-003-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-003-7/}
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