A refinement of multi-dimensional persistence
KEVIN P. KNUDSON · Homology Homotopy and Applications · 2008
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.