Global anomalies on Lorentzian space-times
  We formulate an algebraic criterion for the presence of global anomalies on globally hyperbolic space-times in the framework of locally covariant field theory. We discuss some consequences and check that it reproduces the well-known global $SU(2)$ anomaly in four space-time dimensions. 
Alexander Schenkel, Jochen Zahn
hep-th