  We present the topological solutions of Einstein gravity in the presence of a
non-Abelian Yang-Mills field. In ($n+1$) dimensions, we consider the
$So(n(n-1)/2-1,1)$ semisimple group as the Yang-Mills gauge group, and
introduce the black hole solutions with hyperbolic horizon. We argue that the
4-dimensional solution is exactly the same as the 4-dimensional solution of
Einstein-Maxwell gravity, while the higher-dimensional solutions are new. We
investigate the properties of the higher-dimensional solutions and find that
these solutions in 5 dimensions have the same properties as the topological
5-dimensional solution of Einstein-Maxwell (EM) theory although the metric
function in 5 dimensions is different. But in 6 and higher dimensions, the
topological solutions of EYM and EM gravities with non-negative mass have
different properties. First, the singularity of EYM solution does not present a
naked singularity and is spacelike, while the singularity of topological
Reissner-Nordstrom solution is timelike. Second, there are no extreme 6 or
higher-dimensional black holes in EYM gravity with non-negative mass, while
these kinds of solutions exist in EM gravity. Furthermore, EYM theory has no
static asymptotically de Sitter solution with non-negative mass, while EM
gravity has.
