Topological black holes in the dimensionally continued gravity

We investigate topological black holes in a special class of Lovelock gravity. In odd dimensions, the action is the Chern-Simons form for the anti–de Sitter group. In 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: the 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.