The concept of Cheeger deformations on fiber bundles with compact structure group
Abstract
The purpose of this paper is two-fold: we systematically introduce the notion of Cheeger deformations on fiber bundles with compact structure groups, and recover in a very simple and unified fashion several results that either already appear in the literature or are known by experts, though are not explicitly written elsewhere. We re-prove: Schwachh\"ofer--Tuschmann Theorem on bi-quotients, many results due to Fukaya and Yamaguchi, as well as, naturally extend the work of Searle--Sol\'orzano--Wilhelm on regularization properties of Cheeger deformations, among others. In this sense, this paper should be understood as a survey intended to demonstrate the power of Cheeger deformations. Even though some of the results here appearing may not be known as stated in the presented form, they were already expected, being our contribution to the standardization and spread of the technique via a unique language.
Keywords
Cite
@article{arxiv.1801.06576,
title = {The concept of Cheeger deformations on fiber bundles with compact structure group},
author = {Leonardo F. Cavenaghi and Lino Grama and Llohann D. Sperança},
journal= {arXiv preprint arXiv:1801.06576},
year = {2022}
}
Comments
We have followed anonymous referee criticism and chose to present the paper mostly as a survey, though it does contain original content. This version contains some new references and changes to the abstract and introduction