Abstract
In this chapter we shall examine the action of Möbius transformations in \({{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\mathbb{R}}}}^{2}} \)and their extensions to \({{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\mathbb{R}}}}^{3}} \). We identify ℝ2 with the complex plane ℂ and the algebraic structure of ℂ then allows us to express the action of Möbius transformations algebraically.
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© 1983 Springer Science+Business Media New York
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Beardon, A.F. (1983). Complex Möbius Transformations. 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_4
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DOI: https://doi.org/10.1007/978-1-4612-1146-4_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7022-5
Online ISBN: 978-1-4612-1146-4
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