A refinement of multi-dimensional persistence

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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.
21 pages, 4 figures

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Algebraic Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/131933

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.2608
 http://arxiv.org/abs/0706.2608

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arXiv