Structure of semi-continuous q-tame persistence modules

TL;DR

This paper proves that semi-continuous q-tame persistence modules can be decomposed into simpler interval modules, enhancing understanding of their structure in topological data analysis.

Contribution

It establishes a decomposition theorem for semi-continuous q-tame persistence modules into interval modules, extending prior results using radicals.

Findings

Lower semi-continuous modules decompose as direct sums of intervals.

Upper semi-continuous modules decompose as products of intervals.

Provides a structural characterization of semi-continuous q-tame modules.

Abstract

Using a result by Chazal, Crawley-Boevey and de Silva concerning radicals of persistence modules, we show that every lower semi-continuous q-tame persistence module can be decomposed as a direct sum of interval modules and that every upper semi-continuous q-tame persistence module can be decomposed as a product of interval modules.