Homology, Homotopy and Applications
Volume 24 (2022)
Structure of semi-continuous $q$-tame persistence modules
Pages: 117 – 128
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.
barcode, persistent homology, $q$-tame
2010 Mathematics Subject Classification
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