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arXiv:0706.2608 [math.AT]AbstractReferencesReviewsResources

A refinement of multi-dimensional persistence

Kevin P. Knudson

Published 2007-06-18Version 1

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.

Comments: 21 pages, 4 figures
Categories: math.AT
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