  In this paper, we generalise the treatment of isolated horizons in loop
quantum gravity, resulting in a Chern-Simons theory on the boundary in the
four-dimensional case, to non-distorted isolated horizons in 2(n+1)-dimensional
spacetimes. The key idea is to generalise the four-dimensional isolated horizon
boundary condition by using the Euler topological density of a spatial slice of
the black hole horizon as a measure of distortion. The resulting symplectic
structure on the horizon coincides with the one of higher-dimensional
SO(2(n+1))-Chern-Simons theory in terms of a Peldan-type hybrid connection and
resembles closely the usual treatment in 3+1 dimensions. We comment briefly on
a possible quantisation of the horizon theory. Here, some subtleties arise
since higher-dimensional non-Abelian Chern-Simons theory has local degrees of
freedom. However, when replacing the natural generalisation to higher
dimensions of the usual boundary condition by an equally natural stronger one,
it is conceivable that the problems originating from the local degrees of
freedom are avoided, thus possibly resulting in a finite entropy.
