arXiv:1210.0819 Abstract | arXiv Analytics

arXiv:1210.0819 [math.RT]Abstract References Reviews Resources

Decomposition of pointwise finite-dimensional persistence modules

Published 2012-10-02, updated 2014-07-29Version 3

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.

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

Categories: math.RT

Subjects: 16G20

Keywords: pointwise finite-dimensional persistence modules, decomposition, finite-dimensional vector spaces, direct sum, interval modules

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