Decomposition of pointwise finite-dimensional persistence modules

TL;DR

This paper proves that pointwise finite-dimensional persistence modules over a totally ordered set can be decomposed into simpler interval modules, extending the result to modules with certain chain conditions.

Contribution

It establishes a decomposition theorem for a broad class of persistence modules, generalizing previous results to include modules with the descending chain condition.

Findings

Persistence modules decompose into interval modules

Extension of decomposition to modules with chain conditions

Provides a structural understanding of finite-dimensional persistence modules

Abstract

We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on images and kernels.