An exotic deformation of the hyperbolic space

Nicolas Monod; Pierre Py

doi:10.1353/ajm.2014.0036

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arXiv · 1201.0606

An exotic deformation of the hyperbolic space

Nicolas Monod·Pierre Py

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Abstract

On the one hand, we construct a continuous family of non-isometric proper CAT(-1) spaces on which the isometry group ${\rm Isom}(\mathbf{H}^{n})$ of the real hyperbolic $n$-space acts minimally and cocompactly. This provides the first examples of non-standard CAT(0) model spaces for simple Lie groups. On the other hand, we classify all continuous non-elementary actions of ${\rm Isom}(\mathbf{H}^{n})$ on the infinite-dimensional real hyperbolic space. It turns out that they are in correspondence with the exotic model spaces that we construct.

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Nicolas Monod, Pierre Py. 2012-01-03. An exotic deformation of the hyperbolic space. https://doi.org/10.1353/ajm.2014.0036

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