Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866929500941451264 |
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| author | Lipiński, Michał Kubica, Jacek Mrozek, Marian Wanner, Thomas |
| author_facet | Lipiński, Michał Kubica, Jacek Mrozek, Marian Wanner, Thomas |
| contents | We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in \cite{Mr2017}. The generalization consists in dropping the restrictive assumption in \cite{Mr2017} that every multivector has a unique maximal element. The extension is from the setting of Lefschetz complexes to the more general situation of finite topological spaces. We define isolated invariant sets, isolating neighbourhoods, Conley index and Morse decompositions. We also establish the additivity property of the Conley index and the Morse inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_12698 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces Lipiński, Michał Kubica, Jacek Mrozek, Marian Wanner, Thomas Dynamical Systems Algebraic Topology Combinatorics We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in \cite{Mr2017}. The generalization consists in dropping the restrictive assumption in \cite{Mr2017} that every multivector has a unique maximal element. The extension is from the setting of Lefschetz complexes to the more general situation of finite topological spaces. We define isolated invariant sets, isolating neighbourhoods, Conley index and Morse decompositions. We also establish the additivity property of the Conley index and the Morse inequalities. |
| title | Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces |
| topic | Dynamical Systems Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/1911.12698 |