Loops, Holonomy and Signature
Geometric Topology
2026-04-21 v4 Differential Geometry
Group Theory
Abstract
We show that there is a topology on certain groups of loops in Euclidean space such that these groups are embedded in a Fr\'echet-Lie group which is the structural group of a principal bundle with connection whose holonomy coincides with the Chen signature map. We also give an alternative geometric new proof of the Chen signature theorem and a generalization of this theorem in classes strictly containing the one originally considered by Chen.
Cite
@article{arxiv.2411.12881,
title = {Loops, Holonomy and Signature},
author = {Juan Alonso and Juan Manuel Burgos and Miguel Paternain},
journal= {arXiv preprint arXiv:2411.12881},
year = {2026}
}
Comments
14 pages, no figures. Substantial improvement in presentation, mostly in the introduction, and more details provided