Journal article
The space of barcode bases for persistence modules
- Abstract:
- The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special form. Here we describe a new algorithm for computing barcodes which also keeps track of, and outputs, such a change of basis. Our main result is an explicit characterisation of the group of transformations that sends one barcode basis to another. Armed with knowledge of the entire space of barcode bases, we are able to show that any map of persistence modules can be represented via a partial matching between bars provided that neither source nor target admits nested bars in its barcode. We also generalise the algorithm and results described above to work for zizag modules.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 405.9KB, Terms of use)
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- Publisher copy:
- 10.1007/s41468-022-00094-6
Authors
- Publisher:
- Springer
- Journal:
- Journal of Applied and Computational Topology More from this journal
- Volume:
- 7
- Pages:
- 1–30
- Publication date:
- 2022-07-13
- Acceptance date:
- 2022-05-02
- DOI:
- EISSN:
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2367-1734
- ISSN:
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2367-1726
- Language:
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English
- Keywords:
- Pubs id:
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1256301
- Local pid:
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pubs:1256301
- Deposit date:
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2022-05-06
- ARK identifier:
Terms of use
- Copyright holder:
- Jacquard et al
- Copyright date:
- 2022
- Rights statement:
- © The Author(s) 2022. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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