EVALUATION SUBGROUPS OF HOMOGENEOUS SPACES OF COMPACT LIE GROUPS

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.