Polar Coordinates and Fundamental Group

Jules Chenal

Polar Coordinates and Fundamental Group

Algebraic Topology 2026-07-01 v1

Authors: Jules Chenal

Abstract

In this article, we investigate the relationship between the fundamental group of a space and its continuous transformations. To be more precise, we show that if a continuous action of a Lie group on a space admits a simply connected cross-section, then we can build the universal covering of the space using an extension of the Lie group by a discrete group.

Cite

@article{arxiv.2607.00737,
  title  = {Polar Coordinates and Fundamental Group},
  author = {Jules Chenal},
  journal= {arXiv preprint arXiv:2607.00737},
  year   = {2026}
}