Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

Rational visibility of a Lie group in the monoid of self-homotopy equivalences of a homogeneous space

Pages: 349 – 379

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n1.a14


Katsuhiko Kuribayashi (Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto, Nagano, Japan)


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.


self-homotopy equivalence; homogeneous space; Sullivan model

2010 Mathematics Subject Classification

55P62, 57R19, 57R20, 57T35

Published 12 July 2011