The Connectedness Homomorphism between Discrete Morse Complexes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911953483464704 |
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| author | Zheng, Chong |
| author_facet | Zheng, Chong |
| contents | Given two discrete Morse functions on a simplicial complex, we introduce the {\em connectedness homomorphism} between the corresponding discrete Morse complexes. This concept leads to a novel framework for studying the connectedness in discrete Morse theory at the chain complex level. In particular, we apply it to describe a discrete analogy to `cusp-degeneration' of Morse complexes. A precise comparison between smooth case and our discrete cases is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Connectedness Homomorphism between Discrete Morse Complexes Zheng, Chong Combinatorics Algebraic Topology Given two discrete Morse functions on a simplicial complex, we introduce the {\em connectedness homomorphism} between the corresponding discrete Morse complexes. This concept leads to a novel framework for studying the connectedness in discrete Morse theory at the chain complex level. In particular, we apply it to describe a discrete analogy to `cusp-degeneration' of Morse complexes. A precise comparison between smooth case and our discrete cases is also given. |
| title | The Connectedness Homomorphism between Discrete Morse Complexes |
| topic | Combinatorics Algebraic Topology |
| url | https://arxiv.org/abs/2405.08653 |