Cusps and commensurability classes of hyperbolic 4-manifolds
| dc.contributor.advisor | Reid, Alan W | en_US |
| dc.creator | Sell, Connor | en_US |
| dc.date.accessioned | 2023-08-09T18:05:22Z | en_US |
| dc.date.available | 2023-08-09T18:05:22Z | en_US |
| dc.date.created | 2023-05 | en_US |
| dc.date.issued | 2023-04-21 | en_US |
| dc.date.submitted | May 2023 | en_US |
| dc.date.updated | 2023-08-09T18:05:22Z | en_US |
| dc.description.abstract | It is well-known that the cusp cross-sections of finite-volume, cusped hyperbolic n-manifolds are flat, compact (n-1)-manifolds. In 2002, Long and Reid proved that each of the finitely many homeomorphism classes of flat, compact (n-1)-manifolds occur as the cusp cross-section of some arithmetic hyperbolic n-orbifold; the orbifold was upgraded to a manifold by McReynolds in 2004. There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This thesis provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains a representative with a given cusp type. In particular, for three of the six cusp types, we provide infinitely many examples of commensurability classes that contain no manifolds with cusps of the given type; no such examples were previously known for any cusp type in any dimension. Further, we extend this result to find commensurability classes of hyperbolic 5-manifolds that avoid some compact, flat 4-manifolds as cusp cross-sections, and classes of non-arithmetic manifolds in both dimensions that avoid some cusp types. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Sell, Connor. "Cusps and commensurability classes of hyperbolic 4-manifolds." (2023) Diss., Rice University. <a href="https://hdl.handle.net/1911/115128">https://hdl.handle.net/1911/115128</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/115128 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | geometry | en_US |
| dc.subject | topology | en_US |
| dc.subject | hyperbolic | en_US |
| dc.subject | arithmetic | en_US |
| dc.subject | manifold | en_US |
| dc.title | Cusps and commensurability classes of hyperbolic 4-manifolds | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Mathematics | en_US |
| thesis.degree.discipline | Natural Sciences | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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