Abstract
Proofs are given group theoretically for the absence of the global SU(2) (Witten) anomaly for any compact Lie group GSU(2) satisfying 4(G)=0 (4 is the four-dimensional homotopy group). It is shown that the number of fermion zero modes is even for G=SO(N) (N7) and the five exceptional groups G2, F4, E6, E7, and E8. The absence of the Witten anomaly for the SU(N) (N3) groups requires freedom from the perturbative (triangle) anomaly. © 1987 The American Physical Society.