English

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.

Keywords

Cite

@article{arxiv.0706.2608,
  title  = {A refinement of multi-dimensional persistence},
  author = {Kevin P. Knudson},
  journal= {arXiv preprint arXiv:0706.2608},
  year   = {2007}
}
R2 v1 2026-06-21T08:39:31.077Z