Loops, Holonomy and Signature

Juan Alonso; Juan Manuel Burgos; Miguel Paternain

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arXiv · 2411.12881

Loops, Holonomy and Signature

Juan Alonso·Juan Manuel Burgos·Miguel Paternain

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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.

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Juan Alonso, Juan Manuel Burgos, Miguel Paternain. 2024-11-19. Loops, Holonomy and Signature. https://arxiv.org/abs/2411.12881

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