Generalizations of persistent homology
| dc.contributor.author | McCleary, Alexander J., author | |
| dc.contributor.author | Patel, Amit, advisor | |
| dc.contributor.author | Adams, Henry, committee member | |
| dc.contributor.author | Ben Hur, Asa, committee member | |
| dc.contributor.author | Peterson, Chris, committee member | |
| dc.date.accessioned | 2021-09-06T10:26:33Z | |
| dc.date.available | 2021-09-06T10:26:33Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | Persistent homology typically starts with a filtered chain complex and produces an invariant called the persistence diagram. This invariant summarizes where holes are born and die in the filtration. In the traditional setting the filtered chain complex is a chain complex of vector spaces filtered over a totally ordered set. There are two natural directions to generalize the persistence diagram: we can consider filtrations of more general chain complexes and filtrations over more general partially ordered sets. In this dissertation we develop both of these generalizations by defining persistence diagrams for chain complexes in an essentially small abelian category filtered over any finite lattice. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | McCleary_colostate_0053A_16745.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/233845 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2020- | |
| dc.rights.license | This material is open access and distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 United States License. (https://creativecommons.org/licenses/by-nc-nd/4.0). | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | persistent homology | |
| dc.subject | applied topology | |
| dc.title | Generalizations of persistent homology | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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