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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 wit...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s41468-022-00094-6

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Pembroke College
Role:
Author
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Name:
Engineering and Physical Sciences Research Council
Grant:
EP/R018472/1
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:
2367-1734
ISSN:
2367-1726
Language:
English
Keywords:
Pubs id:
1256301
Local pid:
pubs:1256301
Deposit date:
2022-05-06

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