Cofiltrations of spanning trees in multiparameter persistent homology
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913657129009152 |
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| author | Grimpen, Fritz Stefanou, Anastasios |
| author_facet | Grimpen, Fritz Stefanou, Anastasios |
| contents | Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID coefficients. We propose the use of spanning trees as a tool to identify such generators by introducing a condition for persistent spanning trees, which is accompanied by an existence result for cofiltrations consisting of spanning trees. We also introduce a generalization of spanning trees, called spanning complexes, for dimensions higher than one, and we establish their existence as a first step towards this direction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_00235 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cofiltrations of spanning trees in multiparameter persistent homology Grimpen, Fritz Stefanou, Anastasios Algebraic Topology 55N31 (Primary) 05C50, 05C90 (Secondary) Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID coefficients. We propose the use of spanning trees as a tool to identify such generators by introducing a condition for persistent spanning trees, which is accompanied by an existence result for cofiltrations consisting of spanning trees. We also introduce a generalization of spanning trees, called spanning complexes, for dimensions higher than one, and we establish their existence as a first step towards this direction. |
| title | Cofiltrations of spanning trees in multiparameter persistent homology |
| topic | Algebraic Topology 55N31 (Primary) 05C50, 05C90 (Secondary) |
| url | https://arxiv.org/abs/2312.00235 |