-
An exotic deformation of the hyperbolic space
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 5, October 2014
- pp. 1249-1299
- 10.1353/ajm.2014.0036
- Article
- Additional Information
On the one hand, we construct a continuous family of non-isometric proper ${\rm CAT}(-1)$ spaces on which the
isometry group ${\rm Isom}({\bf H}^n)$ of the real hyperbolic $n$-space acts minimally and cocompactly. This
provides the first examples of non-standard ${\rm CAT}(0)$ model spaces for simple Lie groups. On the other
hand, we classify all continuous non-elementary actions of ${\rm Isom}({\bf H}^n)$ on the infinite-dimensional
real hyperbolic space. It turns out that they are in correspondence with the exotic model spaces that
we construct.