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dc.contributor.authorLeygonie, Jacob
dc.contributor.authorTillmann, Ulrike
dc.date.accessioned2022-04-14T23:30:27Z
dc.date.available2022-04-14T23:30:27Z
dc.date.issued2022-12
dc.identifier.issn0022-4049
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/336112
dc.description.abstractWe study the inverse problem for persistent homology: For a fixed simplicial complex K, we analyse the fiber of the continuous map PH on the space of filters that assigns to a filter f : K Ñ R the total barcode of its associated sublevel set filtration of K. We find that PH is best understood as a map of stratified spaces. Over each stratum of the barcode space the map PH restricts to a (trivial) fiber bundle with fiber a polyhedral complex. Amongst other we derive a bound for the dimension of the fiber depending on the number of distinct endpoints in the barcode. Furthermore, taking the inverse image PH ́1 can be extended to a monodromy functor on the (entrance path) category of barcodes. We demonstrate our theory on the example of the simplicial triangle giving a complete description of all fibers and monodromy maps. This example is rich enough to have a Möbius band as one of its fibers.
dc.publisherElsevier BV
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleThe fiber of persistent homology for simplicial complexes
dc.typeArticle
dc.publisher.departmentIsaac Newton Institute For Mathematical Sciences
dc.date.updated2022-04-12T21:54:37Z
prism.publicationNameJournal of Pure and Applied Algebra
dc.identifier.doi10.17863/CAM.83537
rioxxterms.versionofrecord10.1016/j.jpaa.2022.107099
rioxxterms.versionAM
rioxxterms.typeJournal Article/Review
cam.issuedOnline2022-04-21
cam.orpheus.successMon Sep 12 08:39:47 BST 2022 - Embargo updated*
cam.orpheus.counter14
cam.depositDate2022-04-12
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement
rioxxterms.freetoread.startdate2023-04-21


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Attribution-NonCommercial-NoDerivatives 4.0 International
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial-NoDerivatives 4.0 International