Branching space of precubical set
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912876249219072 |
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| author | Gaucher, Philippe |
| author_facet | Gaucher, Philippe |
| contents | Using the notion of short natural directed path, we introduce the homotopy branching space of a precubical set. It is unique only up to homotopy equivalence. We prove that, for any precubical set, it is homotopy equivalent to the branching space of any q-realization, any m-realization and any h-realization of the precubical set as a flow. As an application, we deduce the invariance of the homotopy branching space and of the branching homology up to cubical subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology of a precubical set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branching space of precubical set Gaucher, Philippe Algebraic Topology Category Theory Using the notion of short natural directed path, we introduce the homotopy branching space of a precubical set. It is unique only up to homotopy equivalence. We prove that, for any precubical set, it is homotopy equivalent to the branching space of any q-realization, any m-realization and any h-realization of the precubical set as a flow. As an application, we deduce the invariance of the homotopy branching space and of the branching homology up to cubical subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology of a precubical set. |
| title | Branching space of precubical set |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2508.14839 |