Homogeneous compact geometries

TL;DR

This paper classifies certain symmetric geometric structures with high symmetry and applies the results to analyze group actions on symmetric spaces.

Contribution

It provides a classification of compact homogeneous geometries of irreducible spherical type and rank at least 2 under transitive compact group actions.

Findings

Classification of compact homogeneous geometries of specified type and rank.

Application of classification to polar actions on symmetric spaces.

Results up to equivariant 2-coverings.

Abstract

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on compact symmetric spaces.