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Hyperbolic Dynamics and Brownian MotionAn Introduction$
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Jacques Franchi and Yves Le Jan

Print publication date: 2012

Print ISBN-13: 9780199654109

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199654109.001.0001

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Kleinian groups

Kleinian groups

Chapter:
(p.80) Chapter Four: Kleinian groups
Source:
Hyperbolic Dynamics and Brownian Motion
Author(s):

Jacques Franchi

Yves Le Jan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199654109.003.0004

This chapter deals with the geometric theory of Kleinian groups and their fundamental domains. It begins with the example of the parabolic tessellation of the hyperbolic plane by means of 2n-gons limited by full geodesic lines (i.e., ideal 2n-gons). Then Dirichlet polyhedra and modular groups are discussed, with Γ(2) and Γ(1) as the main examples.

Keywords:   Kleinian groups, fundamental domains, modular groups

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