Cofiltrations of spanning trees in multiparameter persistent homology

Fritz Grimpen; Anastasios Stefanou

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arXiv · 2312.00235

Cofiltrations of spanning trees in multiparameter persistent homology

Fritz Grimpen·Anastasios Stefanou

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Abstract

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.

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BibTeX RIS

Fritz Grimpen, Anastasios Stefanou. 2023-11-30. Cofiltrations of spanning trees in multiparameter persistent homology. https://arxiv.org/abs/2312.00235

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