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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.14103 |
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| _version_ | 1866911111438139392 |
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| author | Gould, Ben H. |
| author_facet | Gould, Ben H. |
| contents | We investigate the homology of cosheaves over finite simplicial complexes. After constructing the Mayer-Vietoris short exact sequence for this homology theory, we apply discrete Morse theory to this setting, defining the associated Morse chain complex. The main result is the construction of a Morse Mayer-Vietoris short exact sequence of Morse chain complexes, for which we establish a quasi-isomorphism to the standard Mayer-Vietoris sequence. Discussions relating poset-based (co)sheaf definitions to topological ones via Kan extensions and exploring a modern categorical perspective on discrete Morse theory are also included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Morse Mayer-Vietoris Sequence for Cosheaf Homology on Simplicial Complexes Gould, Ben H. Algebraic Topology We investigate the homology of cosheaves over finite simplicial complexes. After constructing the Mayer-Vietoris short exact sequence for this homology theory, we apply discrete Morse theory to this setting, defining the associated Morse chain complex. The main result is the construction of a Morse Mayer-Vietoris short exact sequence of Morse chain complexes, for which we establish a quasi-isomorphism to the standard Mayer-Vietoris sequence. Discussions relating poset-based (co)sheaf definitions to topological ones via Kan extensions and exploring a modern categorical perspective on discrete Morse theory are also included. |
| title | A Morse Mayer-Vietoris Sequence for Cosheaf Homology on Simplicial Complexes |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2508.14103 |