# On the cell structure of flag manifolds

## TL;DR

This paper introduces a unified geometric cell structure for real, complex, and quaternionic flag manifolds, inspired by Milnor and Stasheff's approach for Grassmann manifolds.

## Contribution

It provides a novel, unified geometric method to define cell structures across different types of flag manifolds, extending prior work on Grassmannians.

## Key findings

- Unified cell structure for all three types of flag manifolds
- Method inspired by Milnor and Stasheff's approach
- Potential applications in topology and geometry

## Abstract

We here define a cell structure for real, complex and quaternionic flag manifolds in a unified way. Our method is geometric in nature and is inspired from a method due to Milnor and Stasheff, which they used to define a cell structure for real Grassmann manifolds.