Decomposition of persistence modules
Representation Theory
2019-10-07 v3 Algebraic Topology
Abstract
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.
Cite
@article{arxiv.1811.08946,
title = {Decomposition of persistence modules},
author = {Magnus Bakke Botnan and William Crawley-Boevey},
journal= {arXiv preprint arXiv:1811.08946},
year = {2019}
}
Comments
Very minor edits. To appear in the Proceedings of the AMS