  We apply Dirac's gauge fixing procedure to Chern-Simons theory with gauge
group ISO(2,1) on manifolds RxS, where S is a punctured oriented surface of
general genus. For all gauge fixing conditions that satisfy certain structural
requirements, this yields an explicit description of the Poisson structure on
the moduli space of flat ISO(2,1)-connections on S via the resulting Dirac
bracket. The Dirac bracket is determined by classical dynamical r-matrices for
ISO(2,1). We show that the Poisson structures and classical dynamical
r-matrices arising from different gauge fixing conditions are related by
dynamical ISO(2,1)-valued transformations that generalise the usual gauge
transformations of classical dynamical r-matrices. By means of these
transformations, it is possible to classify all Poisson structures and
classical dynamical r-matrices obtained from such gauge fixings. Generically
these Poisson structures combine classical dynamical r-matrices for
non-conjugate Cartan subalgebras of iso(2,1).
