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arXiv · 2008.02345

Local characterizations for decomposability of 2-parameter persistence modules

Magnus Bakke Botnan·Vadim Lebovici·Steve Oudot
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Abstract

We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topological data analysis. Our indecomposables of interest belong to the so-called interval modules, which by definition are indicator representations of intervals in the poset. While the whole class of interval modules does not admit such a local characterization, we show that the subclass of rectangle modules does admit one and that it is, in some precise sense, the largest subclass to do so.

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Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot. 2022-12-12. Local characterizations for decomposability of 2-parameter persistence modules. https://arxiv.org/abs/2008.02345

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