Kirwan polytopes in the real setting

TL;DR

This paper explores Kirwan's real polytopes within symplectic geometry, focusing on involutions on groups and manifolds, and consolidates previous preprints to advance understanding in this specialized area.

Contribution

It provides a comprehensive study and completion of the theory of Kirwan's real polytopes, integrating prior partial results into a unified framework.

Findings

Complete characterization of Kirwan's real polytopes

Extension of previous partial results

Unified framework for involutions in symplectic geometry

Abstract

This is a monograph devoted to the study of Kirwan's real polytopes, i.e., in the context where there are involutions on the group and on the symplectic manifold. This work brings together and completes the two preprints I had already written on this subject (arXiv:2012.08837, arXiv:2111.13399).