2+1 gravity on the conformal sphere

Understand

We show that there are 2 equivalent first order descriptions of 2+1 gravity with non-zero cosmological constant.

• One is the well-known spacetime description and the other is in terms of evolving conformal geometry.
• The key tool that links these pictures is Cartan geometry, a generalization of Riemannian geometry that allows for geometries locally modelled off arbitrary homogeneous spaces.
• The two different interpretations suggest two distinct phase space reductions.