Chapter

Kleinian groups

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion

Published in print August 2012 | ISBN: 9780199654109
Published online January 2013 | e-ISBN: 9780191745676 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199654109.003.0004

Series: Oxford Mathematical Monographs

Kleinian groups

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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

Chapter.  14323 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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