Hyperbolic Geometry and Distance Functions on Discrete Groups

Details Hyperbolic Geometry and Distance Functions on Discrete Groups Hyperbolic Geometry and Distance Functions on Discrete Groups

2007-12-27

arxiv.org/abs/0712.4294v1

Mathematics

Group Theory

Submitted in partial fulfillment of the requirements of the degree of Bachelor of Science with Honours in Pure Mathematics, Un

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Hyperbolic Geometry and Distance Functions on Discrete Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperbolic Geometry and Distance Functions on Discrete Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic Geometry and Distance Functions on Discrete Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-508032