  We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups
over arbitrary fields and skew fields, with values in the Witt group of
hermitian forms. This cocycle has good functorial properties: it is natural
under extension of scalars and stable, so it can be viewed as a universal
2-dimensional characteristic class for these groups. Over R and C, it coincides
with the first Chern class.
