On the topology of minimal orbits in complex flag manifolds

TL;DR

This paper calculates the Euler-Poincaré characteristic of minimal orbits of real forms acting on complex flag manifolds, providing insights into their topological structure.

Contribution

It introduces a method to compute the Euler-Poincaré characteristic of minimal orbits in complex flag manifolds, advancing understanding of their topology.

Findings

Explicit formulas for Euler-Poincaré characteristics of minimal orbits

Identification of topological invariants of these orbits

Enhanced understanding of the structure of complex flag manifolds

Abstract

We compute the Euler-Poincar\'e characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold.