Geodesic
Rational homotopy via Sullivan models and enriched Lie algebras
Yves Félix1 ; Steve Halperin2
1Université Catholique de Louvain, Louvain-la-Neuve, Belgium
2University of Maryland, Durham, USA
EMS surveys in mathematical sciences, Tome 10 (2023) no. 1, pp. 101-122

Voir la notice de l'article provenant de la source EMS Press

DOI

Rational homotopy theory originated in the late 1960s and the early 1970s with the simultaneous but distinct approaches of Quillen (1969), Sullivan (1977) and Bousfield–Kan (1972). Each approach associated to a path connected space X an “algebraic object” A which is then used to construct a rational completion of X, X→XQ​. These constructions are homotopy equivalent for simply connected CW complexes of finite type, in which case H∗​(XQ​)≅H∗​(X)⊗Q and π∗​(XQ​)≅π∗​(X)⊗Q. Otherwise, they may be different; in fact, Quillen’s construction is only available for simply connected spaces.
DOI : 10.4171/emss/67
Classification : 55-XX
Mots-clés : rational homotopy, Sullivan minimal models

Yves Félix  1   ; Steve Halperin  2

1 Université Catholique de Louvain, Louvain-la-Neuve, Belgium
2 University of Maryland, Durham, USA 
Yves Félix; Steve Halperin. Rational homotopy via Sullivan models and enriched Lie algebras. EMS surveys in mathematical sciences, Tome 10 (2023) no. 1, pp. 101-122. doi: 10.4171/emss/67
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