Hyperbolic Geometry and Distance Functions on Discrete Groups
| dc.creator | Thomas, Anne | |
| dc.date | 2007-12-27 | |
| dc.date.accessioned | 2026-07-07T08:51:33Z | |
| dc.date.available | 2026-07-07T08:51:33Z | |
| dc.description | Chapter 1 is a short history of non-Euclidean geometry, which synthesises my readings of mostly secondary sources. Chapter 2 presents each of the main models of hyperbolic geometry, and describes the tesselation of the upper half-plane induced by the action of $PSL(2,\mathbb{Z})$. Chapter 3 gives background on symmetric spaces and word metrics. Chapter 4 then contains a careful proof of the following theorem of Lubotzky--Mozes--Raghunathan: the word metric on $PSL(2,\mathbb{Z})$ is not Lipschitz equivalent to the metric induced by its action on the associated symmetric space (the upper half-plane), but for $n \geq 3$, these two metrics on $PSL(n,\mathbb{Z})$ are Lipschitz equivalent. | |
| dc.description | Submitted in partial fulfillment of the requirements of the degree of Bachelor of Science with Honours in Pure Mathematics, University of New South Wales, Australia, June 2002. 105 pages | |
| dc.identifier | https://arxiv.org/abs/0712.4294 | |
| dc.identifier | http://arxiv.org/abs/0712.4294 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144972 | |
| dc.subject | Group Theory | |
| dc.subject | History and Overview | |
| dc.title | Hyperbolic Geometry and Distance Functions on Discrete Groups | |
| dc.type | text |