Decomposition of persistence modules

By Magnus Bakke Botnan, W. Crawley‐Boevey. Proceedings of the American Mathematical Society, 2018

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We show that a pointwise finite-dimensional persistence module indexed over a small category decomposes into a direct sum of indecomposables with local endomorphism rings. As an application of this result we give new, short proofs of fundamental structure theorems for persistence modules.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d73f27015c1a4908fb0c7500f13114f9cdc95be3