Resumen de Spaces of locally homogeneous affine surfaces

Miguel Brozos Vázquez , Eduardo García Río , Peter B. Gilkey

• We examine the topology of various spaces of locally homogeneous affine surfaces which arise from the classification result of Opozda (Differ Geom Appl 21:173–198, 2004) as orbits of the action of G L(2, R)(Type A) and the ax+b group (Type B). We determine the topology of the spaces of Type A models in relation to the rank of the Ricci tensor. We determine the topology of the spaces of Type B models which either are flat or where the Ricci tensor is alternating.