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

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

2010-07-23

arxiv.org/abs/1007.4231v1

Mathematics

Algebraic Topology

28 pages

Scientific paper

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. In particular, the visible 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.

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