  We discuss the topological and global gauge properties of the formula for a
black hole entropy due to a purely gravitational Chern-Simons term. We study
under what topological and geometrical conditions this formula is well-defined.
To this end we have to analyze the global properties of the Chern-Simons term
itself and the quantization of its coupling. We show that in some cases the
coupling quantization may interfere with the well-definiteness of the entropy
formula.
