Flat principal 2-group bundles and flat string structures
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866918160596205568 |
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| author | Berwick-Evans, Daniel Cliff, Emily Murray, Laura Nakade, Apurva Phillips, Emma |
| author_facet | Berwick-Evans, Daniel Cliff, Emily Murray, Laura Nakade, Apurva Phillips, Emma |
| contents | For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat 2-group bundles can be described in terms of ordinary $G$-bundles together with a trivialization of a certain 2-gerbe. This specializes to a characterization of flat string structures on vector bundles over differentiable stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_07571 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Flat principal 2-group bundles and flat string structures Berwick-Evans, Daniel Cliff, Emily Murray, Laura Nakade, Apurva Phillips, Emma Algebraic Topology Category Theory For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat 2-group bundles can be described in terms of ordinary $G$-bundles together with a trivialization of a certain 2-gerbe. This specializes to a characterization of flat string structures on vector bundles over differentiable stacks. |
| title | Flat principal 2-group bundles and flat string structures |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2110.07571 |