A refinement of multi-dimensional persistence
Algebraic Topology
2007-06-19 v1
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.
Cite
@article{arxiv.0706.2608,
title = {A refinement of multi-dimensional persistence},
author = {Kevin P. Knudson},
journal= {arXiv preprint arXiv:0706.2608},
year = {2007}
}