Homology, Homotopy and Applications
Volume 10 (2008)
A refinement of multi-dimensional persistence
Pages: 259 – 281
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.