  We consider SU(N) Yang-Mills theories in 2n+1 Euclidean dimensions coupled to
an even flavour-number of Dirac fermions. After integrating out the fermions
the wave functional for the effective Yang-Mills theory inherits a non-trivial
U(1)-connection which is computed in the limit of infinite fermion mass
(adiabatic connection). Its Chern-class turns out to be just half the flavour
number. Its topological origin is explained in the Lagrangean and Hamiltonian
picture.
