  We investigate the topological black holes in a special class of Lovelock
gravity. In the odd dimensions, the action is the Chern-Simons form for the
anti-de Sitter group. In the even dimensions, it is the Euler density
constructed with the Lorentz part of the anti-de Sitter curvature tensor. The
Lovelock coefficients are reduced to two independent parameters: cosmological
constant and gravitational constant. The event horizons of these topological
black holes may have constant positive, zero or negative curvature. Their
thermodynamics is analyzed and electrically charged topological black holes are
also considered. We emphasize the differences due to the different curvatures
of event horizons. As a comparison, we also discuss the topological black holes
in the higher dimensional Einstein-Maxwell theory with a negative cosmological
constant.
