Homology, Homotopy and Applications

Volume 10 (2008)

Number 1

A refinement of multi-dimensional persistence

Pages: 259 – 281

DOI: https://dx.doi.org/10.4310/HHA.2008.v10.n1.a11


Kevin P. Knudson (Department of Mathematics and Statistics, Mississippi State University, Ms., U.S.A.)


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.


persistent homology, Tor group, hypertor group

2010 Mathematics Subject Classification

Primary 55Nxx. Secondary 55Uxx.

Published 1 January 2008