Some basic questions. Why is k "an integer for topological reasons"? (k is a parameter that appears in a second term -- a multiple of the Chern- Simons invariant of the spin connection -- added to the action).
Further, what is "holomorphic" factorization? (A pointer to the basic literature on this will suffice). Is it the only possible constraint?
He argues that the (naive) partition function Z_0(q) differs from the "exact" Z(q) by terms of order O(q). Would this be correct for any k?
He finds that for k=1 the monster group is interpreted as the symmetry of 2+1-dimensional black holes. How sensitive is this result with respect to the value of k, and to respect to the other assuptions used in the derivation?