Repository logo
 

Persistence and simplicial metric thickenings

Simple item page
dc.contributor.authorMoy, Michael, author
dc.contributor.authorAdams, Henry, advisor
dc.contributor.authorPatel, Amit, committee member
dc.contributor.authorPeterson, Christopher, committee member
dc.contributor.authorBen-Hur, Asa, committee member
dc.date.accessioned2024-05-27T10:32:48Z
dc.date.available2024-05-27T10:32:48Z
dc.date.issued2024
dc.description.abstractThis dissertation examines the theory of one-dimensional persistence with an emphasis on simplicial metric thickenings and studies two particular filtrations of simplicial metric thickenings in detail. It gives self-contained proofs of foundational results on one-parameter persistence modules of vector spaces, including interval decomposability, existence of persistence diagrams and barcodes, and the isometry theorem. These results are applied to prove the stability of persistent homology for sublevel set filtrations, simplicial complexes, and simplicial metric thickenings. The filtrations of simplicial metric thickenings studied in detail are the Vietoris–Rips and anti-Vietoris–Rips metric thickenings of the circle. The study of the Vietoris–Rips metric thickenings is motivated by persistent homology and its use in applied topology, and it builds on previous work on their simplicial complex counterparts. On the other hand, the study of the anti-Vietoris–Rips metric thickenings is motivated by their connections to graph colorings. In both cases, the homotopy types of these spaces are shown to be odd-dimensional spheres, with dimensions depending on the scale parameters.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierMoy_colostate_0053A_18234.pdf
dc.identifier.urihttps://hdl.handle.net/10217/238481
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright 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.subjectapplied topology
dc.subjectpersistent homology
dc.subjectVietoris–Rips
dc.subjectpersistence
dc.subjectalgebraic topology
dc.subjecttopological data analysis
dc.titlePersistence and simplicial metric thickenings
dc.typeText
dcterms.rights.dplaThis 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.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Moy_colostate_0053A_18234.pdf
Size:
2.78 MB
Format:
Adobe Portable Document Format
Download

Collections

2020-
Theses and Dissertations