Interval Decomposition of Infinite Zigzag Persistence Modules
Magnus Bakke Botnan
TL;DR
This paper proves that all infinite zigzag persistence modules can be broken down into simpler interval modules, enhancing understanding of their structure in topological data analysis.
Contribution
It introduces a decomposition theorem for infinite zigzag persistence modules, extending the theory of persistence modules to infinite cases.
Findings
Infinite zigzag modules decompose into interval modules
Provides a structural understanding of infinite persistence modules
Extends finite decomposition results to infinite settings
Abstract
We show that every infinite zigzag persistence module decomposes into a direct sum of interval persistence modules.
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