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2011 Rational visibility of a Lie group in the monoid of self-homotopy equivalences of a homogeneous space
Katsuhiko Kuribayashi
Homology Homotopy Appl. 13(1): 349-379 (2011).

Abstract

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.

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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 Appl. 13 (1) 349 - 379, 2011.

Information

Published: 2011
First available in Project Euclid: 29 July 2011

zbMATH: 1247.55006
MathSciNet: MR2803878

Subjects:
Primary: 55P62, 57R19, 57R20, 57T35

Rights: Copyright © 2011 International Press of Boston

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Vol.13 • No. 1 • 2011
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