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arXiv · 1910.03348

An Excision Theorem for Persistent Homology

Megan Palser
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Abstract

We demonstrate that an excision property holds for persistent homology groups. This property holds for a large class of filtrations, and in fact we show that given any filtration on a larger space, we can extend it to a filtration of two subspaces which guarantees that the excision property holds for the triple. This method also applies to the Mayer-Vietoris sequence in persistent homology introduced by DiFabio and Landi in 2011, extending their results to a much larger class of filtrations.

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Megan Palser. 2019-10-08. An Excision Theorem for Persistent Homology. https://arxiv.org/abs/1910.03348

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