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MultiDimensional Apollonian Gaskets

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Abstract

Geometric and group-theoretic approach. Hyperbolic (Lobachevsky) plane L, group G of conformal transformations. Action of the discrete group \(\Gamma _{4}\) on an Apollonian gasket.

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Notes

  1. 1.

    This follows also from (8.1.4), since for externally tangent balls, \(\cos \alpha =\cos \pi = -1\).

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA

    A. A. Kirillov

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  1. A. A. Kirillov
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Kirillov, A.A. (2013). MultiDimensional Apollonian Gaskets. In: A Tale of Two Fractals. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-8382-5_8

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