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Möbius transformations and hyperbolic space in arbitrary dimensions

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Joe Quinn (UANM, Mexico)

We will look at some different methods of generalizing the well-known Möbius transformations of the hyperbolic plane to higher dimensions. We will see a use of Clifford algebras to do this in any dimension, and will compare and contrast this with some alternative quaternion methods that only work up to dimension 5. We'll look briefly at what is special geometrically about the cases up to dimension 5, and how this relates to some recent joint work with Alberto Verjovsky.