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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.01516 |
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| _version_ | 1866914071461232640 |
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| author | Verano, Jagerynn Ting |
| author_facet | Verano, Jagerynn Ting |
| contents | Given a complex of groups, we construct a new class of complex of groups that records its local data and offer a functorial perspective on the statement that complexes of groups are locally developable. We also construct a new notion of an immersion of complexes of groups and establish that a locally isometric immersion of a complex of groups into a non-positively curved complex of groups is $π_1$-injective. Furthermore, the domain complex of groups is developable and the induced map on geometric realizations of developments is an isometric embedding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Immersions of complexes of groups Verano, Jagerynn Ting Group Theory 20F65, 20F67 Given a complex of groups, we construct a new class of complex of groups that records its local data and offer a functorial perspective on the statement that complexes of groups are locally developable. We also construct a new notion of an immersion of complexes of groups and establish that a locally isometric immersion of a complex of groups into a non-positively curved complex of groups is $π_1$-injective. Furthermore, the domain complex of groups is developable and the induced map on geometric realizations of developments is an isometric embedding. |
| title | Immersions of complexes of groups |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2510.01516 |