  The coupling problem of higher spin fields with a non dynamical background is
revisited, focussing our attention in 2+1 dimensional space-time. Starting with
a suitable Lagrangian field formulation, we study causality and the
conservation of local degrees of freedom in a theory with gravitational (no
dynamical) interaction, verifying that this type of theories must be consistent
only in some space-time (i.e., dS/AdS). On the other hand, we consider the
gravitational field as a dynamical object coupled with material fields as
sources, from the point of view of a Yang-Mills gauge formulation for gravity.
There we found some constraints on the shape of material fields and we show
that introduction of auxiliary fields coupled with gauge connection does
eliminate those constraints. The model of a Yang-Mills gauge formulation for
topological massive gravity with cosmological constant is briefly introduced
and we show that its field equations are consistent with the well known
cosmologically extended topological massive gravity of Deser at the torsionless
limit.
