A refinement of multi-dimensional persistence

2007/06/18 by Knudson, Kevin P.
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.0706.2608

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.

Related

• Persistence modules: Algebra and algorithms
• Multidimensional Persistence: Invariants and Parameterization
• Stable resolutions of multi-parameter persistence modules
• Correspondence Modules and Persistence Sheaves: A Unifying Perspective on One-Parameter Persistent Homology
• The Whole in the Parts: Putting nD Persistence Modules Inside Indecomposable (n + 1)D Ones