Abstract
We recall Definition 6.2.2: a Fuchsian group G is a discrete subgroup of ℳ with an invariant disc D (so G acts discontinuously in D). We may assume that the unit disc ▵ (or the half-plane H 2) is G-invariant and so we may regard G as a discrete group of isometries of the hyperbolic plane. We shall see in Chapter 9 that this induces a tesselation, or “tiling,” of the plane by hyperbolic polygons and it is the geometry of this action of G which, from now on, is our only concern.
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© 1983 Springer Science+Business Media New York
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Beardon, A.F. (1983). Fuchsian Groups. In: The Geometry of Discrete Groups. Graduate Texts in Mathematics, vol 91. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1146-4_8
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DOI: https://doi.org/10.1007/978-1-4612-1146-4_8
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