On Eschenburg's Habilitation on Biquotients

TL;DR

This paper summarizes Jost Eschenburg's habilitation on biquotients, highlighting results on positive curvature examples, classification of equal rank biquotients, and providing valuable but less accessible insights into the topic.

Contribution

It compiles and clarifies Eschenburg's results on biquotients and their classifications, making them more accessible to the mathematical community.

Findings

Classification of equal rank biquotients of simple Lie groups

New examples of biquotients with positive curvature

Comprehensive overview of biquotients in Riemannian geometry

Abstract

These are notes of a talk I gave in a seminar at the University of Pennsylvania summarizing results in the Habilitation by Jost Eschenburg on "Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekruemmten Orbitraeumen". Due to the fact that it is published in a not easily accesible journal (and is written in German) some of the results of his Habilitation are not as well known as they deserve. Although the main results on new examples with positive curvature were later published elsewhere, it contains a wealth of further information about biquotients and a classification of equal rank biquotients of simple Lie groups. I have no intention to publish these notes, but post them as a service to the public. A scanned version of his Habilitation (written in German) is available on my homepage.