An exotic deformation of the hyperbolic space

Details An exotic deformation of the hyperbolic space An exotic deformation of the hyperbolic space

2012-01-03

arxiv.org/abs/1201.0606v2

Mathematics

Geometric Topology

36 pages, minor modifications (including a change in the title)

Scientific paper

We construct a continuous family of non-isometric proper CAT(-1) spaces on which the isometry group Isom(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. We also classify all continuous non-elementary actions of Isom(H^n) on the infinite-dimensional real hyperbolic space.

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