Geodesic
Rational visibility of a Lie group in the monoid of self-homotopy equivalences of a homogeneous space
Homology, homotopy, and applications, Tome 13 (2011) no. 1, pp. 349-379.

Voir la notice de l'article provenant de la source International Press of Boston

Let $M$ be a homogeneous space admitting a left translation by a connected Lie group $G$. The adjoint to the action gives rise to a map from $G$ to the monoid of self-homotopy equivalences of $M$. The purpose of this paper is to investigate the injectivity of the homomorphism which is induced by the adjoint map on the rational homotopy group. In particular, the visibility degrees are determined explicitly for all the cases of simple Lie groups and their associated homogeneous spaces of rank one which are classified by Oniscik.
DOI : 10.4310/HHA.2011.v13.n1.a14
Classification : 55P62, 57R19, 57R20, 57T35
Keywords: self-homotopy equivalence, homogeneous space, Sullivan model 
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     title = {Rational visibility of a {Lie} group in the monoid of self-homotopy equivalences of a homogeneous space},
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     pages = {349--379},
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Katsuhiko Kuribayashi. Rational visibility of a Lie group in the monoid of self-homotopy equivalences of a homogeneous space. Homology, homotopy, and applications, Tome 13 (2011) no. 1, pp. 349-379. doi : 10.4310/HHA.2011.v13.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2011.v13.n1.a14/

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