THE FIBER OF PERSISTENT HOMOLOGY FOR SIMPLICIAL COMPLEXES
dc.contributor.author | Tillmann, Ulrike | |
dc.contributor.author | Leygonie, Jacob | |
dc.date.accessioned | 2022-04-14T23:30:27Z | |
dc.date.available | 2022-04-14T23:30:27Z | |
dc.identifier.issn | 0022-4049 | |
dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/336112 | |
dc.description.abstract | We 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.publisher | Elsevier | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.title | THE FIBER OF PERSISTENT HOMOLOGY FOR SIMPLICIAL COMPLEXES | |
dc.type | Article | |
dc.publisher.department | Isaac Newton Institute For Mathematical Sciences | |
dc.date.updated | 2022-04-12T21:54:37Z | |
prism.publicationName | Journal of Pure and Applied Algebra | |
dc.identifier.doi | 10.17863/CAM.83537 | |
rioxxterms.version | AM | |
rioxxterms.type | Journal Article/Review | |
cam.orpheus.counter | 6 | * |
cam.depositDate | 2022-04-12 | |
pubs.licence-identifier | apollo-deposit-licence-2-1 | |
pubs.licence-display-name | Apollo Repository Deposit Licence Agreement | |
rioxxterms.freetoread.startdate | 2025-04-14 |
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