| dc.rights.license | CC-BY-NC-ND | |
| dc.contributor.advisor | Meier, F.L.M. | |
| dc.contributor.author | Brink, Christiaan van den | |
| dc.date.accessioned | 2022-08-16T00:01:17Z | |
| dc.date.available | 2022-08-16T00:01:17Z | |
| dc.date.issued | 2022 | |
| dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/42302 | |
| dc.description.abstract | Assuming general position, Bauer and Edelsbrunner show that the Cech complex collapses into the Delaunay complex for point sets in Euclidean space. By allowing non-unique solutions to certain minimal spheres, we bypass this assumption. Furthermore, using recursion, we prove an equivariant version of the collapsing theorem restricted to the plane assuming the point cloud has symmetry. We also discuss a simple symmetrical point cloud configuration in the plane that induces an indecomposable reducible representation on the barcode decomposition of a symmetric Delaunay complexes. | |
| dc.description.sponsorship | Utrecht University | |
| dc.language.iso | EN | |
| dc.subject | This thesis proves that the Cech complex collapses into the Delaunay complex for arbitrary finite point configurations in Euclidean space. Previously, this was only known for points in general position. Furthermore, if the point set is a symmetrical subset of the plane with respect to a finite orthogonal group, then we prove that the collapse can be chosen to be equivariant as well. | |
| dc.title | Collapsing theorem for Delaunay complexes in non-general position and symmetry | |
| dc.type.content | Master Thesis | |
| dc.rights.accessrights | Open Access | |
| dc.subject.keywords | Non-general position; Simplicial collapse; Cech complex; Delaunay complex; Minimal excluding spheres; Equivariant simplicial collapse; Topological Data Analysis; Symmetrical data; | |
| dc.subject.courseuu | Mathematical Sciences | |
| dc.thesis.id | 8511 | |
