Cusps and commensurability classes of hyperbolic 4-manifolds

Simple item page
dc.contributor.advisorReid, Alan W
dc.creatorSell, Connor
dc.date.accessioned2023-08-09T18:05:22Z
dc.date.available2023-08-09T18:05:22Z
dc.date.created2023-05
dc.date.issued2023-04-21
dc.date.submittedMay 2023
dc.date.updated2023-08-09T18:05:22Z
dc.description.abstractIt 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.
dc.format.mimetypeapplication/pdf
dc.identifier.citationSell, 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>.
dc.identifier.urihttps://hdl.handle.net/1911/115128
dc.language.isoeng
dc.rightsCopyright 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.
dc.subjectgeometry
dc.subjecttopology
dc.subjecthyperbolic
dc.subjectarithmetic
dc.subjectmanifold
dc.titleCusps and commensurability classes of hyperbolic 4-manifolds
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
SELL-DOCUMENT-2023.pdf
Size:
1.6 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.84 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.6 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Electronic Theses and Dissertations