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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_2017_003_7,
     author = {Buijs, Urtzi and F\'elix, Yves and Murillo, Aniceto and Tanr\'e, Daniel},
     title = {Maurer{\textendash}Cartan {Elements} in the {Lie} {Models} of {Finite} {Simplicial} {Complexes}},
     journal = {Canadian mathematical bulletin},
     pages = {470--477},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2017-003-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-003-7/}
}
TY  - JOUR
AU  - Buijs, Urtzi
AU  - Félix, Yves
AU  - Murillo, Aniceto
AU  - Tanré, Daniel
TI  - Maurer–Cartan Elements in the Lie Models of Finite Simplicial Complexes
JO  - Canadian mathematical bulletin
PY  - 2017
SP  - 470
EP  - 477
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-003-7/
DO  - 10.4153/CMB-2017-003-7
ID  - 10_4153_CMB_2017_003_7
ER  - 
%0 Journal Article
%A Buijs, Urtzi
%A Félix, Yves
%A Murillo, Aniceto
%A Tanré, Daniel
%T Maurer–Cartan Elements in the Lie Models of Finite Simplicial Complexes
%J Canadian mathematical bulletin
%D 2017
%P 470-477
%V 60
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-003-7/
%R 10.4153/CMB-2017-003-7
%F 10_4153_CMB_2017_003_7

[1] [1] Buijs, U., Felix, Y., Murillo, A., and Tanre, D., Lie models of simplicial sets and representability of the Quillen functor. arxiv:1 508.01442 Google Scholar

[2] [2] Buijs, U., Felix, Y., Murillo, A., and Tanre, D., The Deligne groupoid of the Lawrence-Sullivan interval. Topology Appl. 204(2016), 1–7. http://dx.doi.Org/10.101 6/j.topol.201 6.02.004 Google Scholar

[3] [3] Buijs, U., Felix, Y., Murillo, A., and Tanre, D., Rational Lie models for non-simply connected spaces and Bousfield-Kan completion. arxiv:1 601.05331 Google Scholar

[4] [4] Buijs, U. and Murillo, A., The Lawrence-Sullivan interval is the right model ofl+. Algebr. Geom. Topol. 13(2013), no. 1, 577–588. http://dx.doi.Org/10.2140/agt.2013.13.577 Google Scholar

[5] [5] Felix, Y., Halperin, S., and Thomas, J.-C., Rational homotopy theory. Graduate Texts in Mathematics, 205, Springer-Verlag, New York, 2001. http://dx.doi.Org/10.1007/978-1 -4613-0105-9 Google Scholar

[6] [6] Felix, Y., Halperin, S., and Thomas, J.-C., Rational homotopy theory. II. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015. http://dx.doi.Org/10.1142/9473 Google Scholar

[7] [7] Gomez-Tato, A., Halperin, S., and Tanre, D., Rational homotopy theory for non-simply connected spaces. Trans. Amer. Math. Soc. 352(2000), no. 4,1493-1525. http://dx.doi.Org/10.1090/S0002-9947-99-02463-0 Google Scholar

[8] [8] Lawrence, R. and Sullivan, D., A formula for topology/deformations and its significance. Fund. Math. 225(2014), no. 1, 229–242. http://dx.doi.Org/10.4064/fm225-1-10 Google Scholar

[9] [9] Parent, P.-E. and Tanre, D., Lawrence-Sullivan models for the interval. Topology Appl. 159(2012), no. 1, 371–378. http://dx.doi.Org/10.101 6/j.topol.2011.1 0.006 Google Scholar

[10] [10] Quillen, D., Rational homotopy theory. Ann. of Math. (2) 90(1969), 205–295. http://dx.doi.Org/10.2307/1 970725 Google Scholar

[11] [11] Sullivan, D., Infinitesimal computations in topology. Inst. Hautes Etudes Sci. Publ. Math. 47(1977), 269–331. Google Scholar

[12] [12] Tanre, D., Homotopie rationnelle: modeles de Chen, Quillen, Sullivan. Lecture Notes in Mathematics, 1025, Springer-Verlag, Berlin, 1983. http://dx.doi.Org/!0.1007/BFb0071482 Google Scholar

Cité par Sources :