  We present the alternative topological twisting of N=4 Yang-Mills, in which
the path integral is dominated not by instantons, but by flat connections of
the COMPLEXIFIED gauge group. The theory is nontrivial on compact orientable
four-manifolds with nonpositive Euler number, which are necessarily not simply
connected. On such manifolds, one finds a single topological invariant,
analogous to the Casson invariant of three-manifolds.
