Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2010.03913 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916579640344576 |
|---|---|
| author | Pap, Eric J. Waalkens, Holger |
| author_facet | Pap, Eric J. Waalkens, Holger |
| contents | We study fiber bundles where the fibers are not a group $G$, but a free $G$-space with disjoint orbits. These bundles closely resemble principal bundles, hence we call them semi-principal bundles. The study of such bundles is facilitated by defining the notion of a basis of a $G$-set, in analogy with a basis of a vector space. The symmetry group of these bases is a wreath product. Similar to vector bundles, using the notion of a basis induces a frame bundle construction, which in this case results in a principal bundle with the wreath product as structure group. This construction can be formalized in the language of a functor, which retracts the semi-principal bundles to the principal bundles. In addition, semi-principal bundles support parallel transport just like principal bundles, and this carries over to the frame bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_03913 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Frames of group-sets and their application in bundle theory Pap, Eric J. Waalkens, Holger Differential Geometry 55R10, 57M60 We study fiber bundles where the fibers are not a group $G$, but a free $G$-space with disjoint orbits. These bundles closely resemble principal bundles, hence we call them semi-principal bundles. The study of such bundles is facilitated by defining the notion of a basis of a $G$-set, in analogy with a basis of a vector space. The symmetry group of these bases is a wreath product. Similar to vector bundles, using the notion of a basis induces a frame bundle construction, which in this case results in a principal bundle with the wreath product as structure group. This construction can be formalized in the language of a functor, which retracts the semi-principal bundles to the principal bundles. In addition, semi-principal bundles support parallel transport just like principal bundles, and this carries over to the frame bundle. |
| title | Frames of group-sets and their application in bundle theory |
| topic | Differential Geometry 55R10, 57M60 |
| url | https://arxiv.org/abs/2010.03913 |