Detecting Hilbert manifolds among isometrically homogeneous metric spaces

TL;DR

This paper develops criteria to identify Hilbert manifolds within isometrically homogeneous metric spaces and applies these criteria to classify certain homogeneous spaces G/H as Hilbert manifolds.

Contribution

It introduces new methods for recognizing Hilbert manifolds in isometrically homogeneous metric spaces and extends these results to homogeneous spaces of topological groups.

Findings

Criteria for detecting Hilbert manifolds in homogeneous metric spaces

Application of criteria to classify G/H as Hilbert manifolds

Advancement in understanding the structure of homogeneous spaces

Abstract

We detect Hilbert manifolds among isometrically homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed balanced subgroup of G.