Abstract
This last chapter is a very brief introduction to the study of a particularly nice class of subgroups of Möb(ℍ), the discrete subgroups. After defining discreteness, we describe a means of constructing a picture of a discrete group, namely its fundamental polygon. We close by giving a special case of Poincaré’s polygon theorem, which gives conditions for a hyperbolic polygon to be the fundamental polygon of a discrete group.
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© 1999 Springer-Verlag London
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Anderson, J.W. (1999). Groups Acting on ℍ. In: Hyperbolic Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-3987-4_6
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DOI: https://doi.org/10.1007/978-1-4471-3987-4_6
Publisher Name: Springer, London
Print ISBN: 978-1-85233-156-6
Online ISBN: 978-1-4471-3987-4
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