Riemannian submersions from simple, compact Lie groups

TL;DR

This paper constructs numerous examples of Riemannian submersions from simple, compact Lie groups that are not quotients by group actions, addressing a question posed by K. Grove.

Contribution

It provides infinitely many explicit examples of Riemannian submersions from simple, compact Lie groups that are not group quotients, expanding understanding of such mappings.

Findings

Constructed infinitely many Riemannian submersions from Lie groups

Examples are not quotients of the groups by any group action

Addresses a specific open question in the field

Abstract

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses a question of K. Grove's about Riemannian submersions from Lie groups.