Branching space of multipointed d-space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914305259077632 |
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| author | Gaucher, Philippe |
| author_facet | Gaucher, Philippe |
| contents | Using the notion of short directed path, we introduce the branching space of a multipointed $d$-space. We prove that for any q-cofibrant multipointed $d$-space, it is homeomorphic to the branching space of the q-cofibrant flow obtained by applying the categorization functor. As an application, we deduce a purely topological proof of the invariance of the branching space and of the branching homology of cellular multipointed $d$-spaces up to globular subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branching space of multipointed d-space Gaucher, Philippe Algebraic Topology Category Theory Using the notion of short directed path, we introduce the branching space of a multipointed $d$-space. We prove that for any q-cofibrant multipointed $d$-space, it is homeomorphic to the branching space of the q-cofibrant flow obtained by applying the categorization functor. As an application, we deduce a purely topological proof of the invariance of the branching space and of the branching homology of cellular multipointed $d$-spaces up to globular subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology. |
| title | Branching space of multipointed d-space |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2507.08377 |