Decomposition of pointwise finite-dimensional persistence modules
Representation Theory
2014-07-30 v3
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.
Cite
@article{arxiv.1210.0819,
title = {Decomposition of pointwise finite-dimensional persistence modules},
author = {William Crawley-Boevey},
journal= {arXiv preprint arXiv:1210.0819},
year = {2014}
}
Comments
Changes in v3 (at request of a referee): more discussion of persistent homology and barcodes; some results mentioned in the introduction now formulated as corollaries