dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Mesland, B. | |
dc.contributor.author | Smeenk, S. | |
dc.date.accessioned | 2021-08-27T18:00:15Z | |
dc.date.available | 2021-08-27T18:00:15Z | |
dc.date.issued | 2021 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/41301 | |
dc.description.abstract | This thesis explores the possibility of defining `non-commutative persistent homology'. Persistent homology is an algorithm in topological data analysis that assigns to each point cloud a `barcode' which contains information about the shape of this point cloud. An important property of the persistent homology map is that it is stable: it is Lipschitz-continuous with respect to the Gromov-Hausdorff distance on point clouds and the 'bottleneck distance' on barcodes. In `non-commutative persistent homology' we aim to formulate persistent homology using non-commutative geometry. We introduce non-commutative metrics, non-commutative Gromov-Hausdorff distances and we formulate versions of non-commutative vertex sets based on the algebraic generalization of points in a topological space. Using this framework we produce four candidate non-commutative persistent homology maps defined on non-commutative metric spaces. The first candidate is demonstrated to be ineligible, as it does satisfy the stability property. The second candidate is shown to be ill-defined. For the remaining candidates the well-definedness (a fortiori the eligibility) remains open. | |
dc.description.sponsorship | Utrecht University | |
dc.format.extent | 1214997 | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Non-commutative Persistent Homology | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | persistent homology, topological data analysis, TDA, non-commutative geometry, NCG, Lip-norm, Gromov-Hausdorff, quantum Gromov-Hausdorff, non-commutative metric | |
dc.subject.courseuu | Mathematical Sciences | |