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  Persistence Steenrod modules

Lupo, U., Medina-Mardones, A. M., & Tauzin, G. (2022). Persistence Steenrod modules. Journal of Applied and Computational Topology, 6(4), 475-502. doi:10.1007/s41468-022-00093-7.

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arXiv:1812.05031.pdf (Preprint), 717KB
 
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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.

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 Creators:
Lupo, Umberto, Author
Medina-Mardones, Anibal M.1, Author           
Tauzin, Guillaume, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Topology
 Abstract: It has long been envisioned that the strength of the barcode invariant of
filtered cellular complexes could be increased using cohomology operations.
Leveraging recent advances in the computation of Steenrod squares, we introduce
a new family of computable invariants on mod 2 persistent cohomology termed
$Sq^k$-barcodes. We present a complete algorithmic pipeline for their
computation and illustrate their real-world applicability using the space of
conformations of the cyclo-octane molecule.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
 Pages: 28
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1812.05031
DOI: 10.1007/s41468-022-00093-7
 Degree: -

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Title: Journal of Applied and Computational Topology
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 6 (4) Sequence Number: - Start / End Page: 475 - 502 Identifier: -