Evaluation subgroups of homogeneous spaces of compact Lie groups

Jin Ho Lee; Kee Young Lee

doi:10.4134/BKMS.2013.50.5.1725

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(5): 1725-1736

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1725

Evaluation subgroups of homogeneous spaces of compact Lie groups

Jin Ho Lee and Kee Young Lee

Korea University, Korea University

Abstract

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Abstract

In this paper, we compute the images of homotopy groups of various classical Lie groups under the homomorphisms induced by the natural projections from those groups to irreducible symmetric spaces of classical type. We identify that those computations are certain lower bounds of Gottlieb groups of irreducible symmetric spaces. We use the lower bounds to compute some Gottlieb groups.

Keywords: evaluation subgroup, symmetric spaces, stable homotopy groups

MSC numbers: 55Q52, 55Q70, 55Q10