Brozos Vázquez, MiguelGarcía Río, EduardoGilkey, Peter2024-05-022024-05-022020Brozos-Vázquez, M., García-Río, E. & Gilkey, P. Spaces of locally homogeneous affine surfaces. RACSAM 114, 39 (2020)http://hdl.handle.net/10347/33746This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s13398-019-00763-9We examine the topology of various spaces of locally homogeneous affine surfaces which arise from the classification result of Opozda [11] as orbits of the action of GL(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.engHomogeneous affine surfaceLinear equivalenceRicci tensorjournal article10.1007/s13398-019-00763-9open access