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Geometry and Dynamics of Groups and Spaces pp 487–564Cite as

Kleinian Groups in Higher Dimensions

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Part of the book series: Progress in Mathematics ((PM,volume 265))

Abstract

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space ℍn for n ≥ 4. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of ℍ3.

To the memory of Sasha Reznikov

During this work the I was partially supported by various NSF grants, especially DMS-8902619 at the University of Maryland and DMS-04-05180 at UC Davis. Most of this work was done when I was visiting the Max Plank Institute for Mathematics in Bonn.

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  1. Department of Mathematics, University of California, Davis, CA, 95616, USA

    Michael Kapovich

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  1. Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT, 06520, USA

    Mikhail Kapranov

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Yuri Ivanovich Manin  & Pieter Moree  & 

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka, 3, 01601, Kyiv, Ukraine

    Sergiy Kolyada

  4. UFR de Mathématiques, Université de Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    Leonid Potyagailo

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Kapovich, M. (2007). Kleinian Groups in Higher Dimensions. In: Kapranov, M., Manin, Y.I., Moree, P., Kolyada, S., Potyagailo, L. (eds) Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol 265. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8608-5_13

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