Gaona, Tyler
(2022)
On hyperbolic 3-orbifolds of small volume.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
This thesis is concerned with hyperbolic 3-orbifolds of small volume. An n-orbifold is a space which locally, i.e. in a neighborhood of any point, looks like a quotient of Euclidean space \(\mb{R}^n\). We are interested in those spaces which may be equipped with hyperbolic geometry, i.e. are locally modeled on the quotient \(\mb{H}^n\) by a discrete subgroup of its isometries. Following the work of Meyerhoff and Adams we classify minimal volume orbifolds with one rigid and one nonrigid cusp. We then discuss joint work with J. DeBlois, A. H. Ekanayake, M. Fincher, A. Gharagozlou, and P. Mondal on establishing a census of orbifolds commensurable with the figure eight knot complement.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
30 September 2022 |
| Date Type: |
Publication |
| Defense Date: |
13 July 2022 |
| Approval Date: |
30 September 2022 |
| Submission Date: |
29 July 2022 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
114 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
hyperbolic geometry
orbifold
cusp
commensurable |
| Additional Information: |
draft |
| Date Deposited: |
30 Sep 2022 19:02 |
| Last Modified: |
30 Nov 2022 12:46 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/43411 |
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