  It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons
theory, with the gauge group given by the local isometry group, depending on
the metric signature and the cosmological constant. Point particles are added
into spacetime as (spinning) conical defects. Then, in principle, one may
integrate out the gravitational degrees of freedom to obtain the effective
particle action; the most interesting consequence is that the momentum space of
a particle turns out to be curved. This is still not completely understood in
the case of non-zero cosmological constant.
