The Banach-Tarski paradox for flag manifolds

TL;DR

This paper extends the Banach-Tarski paradox from the 2-sphere to flag manifolds, demonstrating that classical groups can act paradoxically on these more complex geometric structures.

Contribution

It generalizes the Banach-Tarski paradox to flag manifolds, broadening the scope of paradoxical group actions beyond spheres.

Findings

Classical groups act paradoxically on flag manifolds

Extension of Banach-Tarski paradox to new geometric settings

Demonstrates paradoxical decompositions in higher-dimensional structures

Abstract

The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.