  In this note we study the structure of diffeomorphism anomalies in 3+1
canonical gravity coupled to a chiral massless fermion. We find that when the
spatial manifold is S^3 or a Lens space L(p,q), the first homotopy group of the
related diffeomorphism group can be nontrivial and hence the question of global
anomalies becomes relevant. Here we show that for gravity coupled to SU(2)
chiral fermions, assuming the strong form of the Hatcher conjecture,
SU(2)-induced diffeomorphism anomalies do not occur whenever the spatial
manifold is S^3 or a Lens space.
