Defining persistence diagrams for cohomology of a cofiltration indexed over a finite lattice
| dc.contributor.author | Rask, Tatum D., author | |
| dc.contributor.author | Patel, Amit, advisor | |
| dc.contributor.author | Shoemaker, Mark, committee member | |
| dc.contributor.author | Tucker, Dustin, committee member | |
| dc.date.accessioned | 2023-01-21T01:24:09Z | |
| dc.date.available | 2023-01-21T01:24:09Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | Persistent homology and cohomology are important tools in topological data analysis, allowing us to track how homological features change as we move through a filtration of a space. Original work in the area focused on filtrations indexed over a totally ordered set, but more recent work has been done to generalize persistent homology. In one avenue of generalization, McCleary and Patel prove functoriality and stability of persistent homology of a filtration indexed over any finite lattice. In this thesis, we show a similar result for persistent cohomology of a cofiltration. That is, for P a finite lattice and F : P → ▽K a cofiltration, the nth persistence diagram is defined as the Möbius inversion of the nth birth-death function. We show that, much like in the setting of persistent homology of a filtration, this composition is functorial and stable with respect to the edit distance. With a general definition of persistent cohomology, we hope to discover whether duality theorems from 1-parameter persistence generalize to more general lattices. | |
| dc.format.medium | born digital | |
| dc.format.medium | masters theses | |
| dc.identifier | Rask_colostate_0053N_17503.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/235954 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2020- | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject | cohomology | |
| dc.subject | algebraic topology | |
| dc.subject | persistence | |
| dc.title | Defining persistence diagrams for cohomology of a cofiltration indexed over a finite lattice | |
| dc.type | Text | |
| dc.type | Image | |
| 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 | Masters | |
| thesis.degree.name | Master of Science (M.S.) |
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