Loops, Holonomy and Signature

2024/11/19 by Juan Alonso, Alonso, Juan, Juan Manuel Burgos +3
Physics and Astronomy · #51H25 #53C29 #55P10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Historical Astronomy and Related Studies

paper · pdf · doi:10.48550/arxiv.2411.12881

openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there is a topology on certain groups of loops in Euclidean space such that these groups are embedded in a Fréchet-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.

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