3-manifolds algorithmically bound 4-manifolds
| dc.contributor.author | Churchill, Samuel | |
| dc.contributor.supervisor | Mehlenbacher, Alan | |
| dc.contributor.supervisor | Budney, Ryan David | |
| dc.date.accessioned | 2019-08-27T22:39:21Z | |
| dc.date.available | 2019-08-27T22:39:21Z | |
| dc.date.copyright | 2019 | en_US |
| dc.date.issued | 2019-08-27 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | This thesis presents an algorithm for producing 4–manifold triangulations with boundary an arbitrary orientable, closed, triangulated 3–manifold. The research is an extension of Costantino and Thurston’s work on determining upper bounds on the number of 4–dimensional simplices necessary to construct such a triangulation. Our first step in this bordism construction is the geometric partitioning of an initial 3–manifold M using smooth singularity theory. This partition provides handle attachment sites on the 4–manifold Mx[0,1] and the ensuing handle attachments eliminate one of the boundary components of Mx[0,1], yielding a 4-manifold with boundary exactly M. We first present the construction in the smooth case before extending the smooth singularity theory to triangulated 3–manifolds. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/11069 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | Topology | en_US |
| dc.subject | Geometric Topology | en_US |
| dc.subject | Computational Topology | en_US |
| dc.subject | Low-Dimensional Topology | en_US |
| dc.subject | 3-manifold | en_US |
| dc.subject | 4-manifold | en_US |
| dc.subject | Triangulation | en_US |
| dc.subject | Algorithmic Construction | en_US |
| dc.title | 3-manifolds algorithmically bound 4-manifolds | en_US |
| dc.type | Thesis | en_US |