  We consider various models of three-dimensional gravity with torsion or
nonmetricity (metric affine gravity), and show that they can be written as
Chern-Simons theories with suitable gauge groups. Using the groups ISO(2,1),
SL(2,C) or SL(2,R) x SL(2,R), and the fact that they admit two independent
coupling constants, we obtain the Mielke-Baekler model for zero, positive or
negative effective cosmological constant respectively. Choosing SO(3,2) as
gauge group, one gets a generalization of conformal gravity that has zero
torsion and only the trace part of the nonmetricity. This characterizes a Weyl
structure. Finally, we present a new topological model of metric affine gravity
in three dimensions arising from an SL(4,R) Chern-Simons theory.

High Energy Physics - Theory;General Relativity and Quantum Cosmology