Loops, Holonomy and Signature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918452698021888 |
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| author | Alonso, Juan Burgos, Juan Manuel Paternain, Miguel |
| author_facet | Alonso, Juan Burgos, Juan Manuel Paternain, Miguel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loops, Holonomy and Signature Alonso, Juan Burgos, Juan Manuel Paternain, Miguel Geometric Topology Differential Geometry Group Theory 53C29, 55P10, 51H25 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. |
| title | Loops, Holonomy and Signature |
| topic | Geometric Topology Differential Geometry Group Theory 53C29, 55P10, 51H25 |
| url | https://arxiv.org/abs/2411.12881 |