A refinement of multi-dimensional persistence

Kevin P. Knudson

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arXiv · 0706.2608

A refinement of multi-dimensional persistence

Kevin P. Knudson

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Abstract

We study the multi-dimensional persistence of Carlsson and Zomorodian and obtain a finer classification based upon the higher tor-modules of a persistence module. We propose a variety structure on the set of isomorphism classes of these modules, and present several examples. We also provide a geometric interpretation for the higher tor-modules of homology modules of multi-filtered simplicial complexes.

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Kevin P. Knudson. 2007-06-18. A refinement of multi-dimensional persistence. https://arxiv.org/abs/0706.2608

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