One Formulation for both Lineal Gravities through a Dimensional Reduction

The two lineal gravities — based on the de Sitter group or a central extension of the Poincar'e group in 1+1 dimensions — are shown to derive classically from a unique topological gauge theory. This one is obtained after a dimensional reduction of a Chern–Simons model, which describes pure gravity in 2+1 dimensions, the gauge symmetry being given by an extension of ISO(2,1).