Homology, Homotopy and Applications

Volume 24 (2022)

Number 1

Structure of semi-continuous $q$-tame persistence modules

Pages: 117 – 128

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n1.a6

Author

Maximilian Schmahl (Mathematisches Institut, Universität Heidelberg, Germany)

Abstract

Using a result by Chazal, Crawley–Boevey and de Silva concerning radicals of persistence modules, we show that every lower semi-continuous $q$-tame persistence module can be decomposed as a direct sum of interval modules and that every upper semi-continuous $q$-tame persistence module can be decomposed as a product of interval modules.

Keywords

barcode, persistent homology, $q$-tame

2010 Mathematics Subject Classification

16G20, 55Nxx

Full Text (PDF format)

Copyright © 2022, Maximilian Schmahl. Permission to copy for private use granted.

This research was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany’s Excellence Strategy EXC-2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster), the Transregional Colloborative Research Center CRC/TRR 191 (281071066) and the Research Training Group RTG 2229 (281869850).

Received 16 October 2020

Received revised 13 February 2021

Accepted 26 February 2021

Published 6 April 2022