An equivariant deformation retraction of the Thurston spine

This paper shows that there is a mapping class group-equivariant deformation retraction of the Teichmüller space of a closed, orientable surface onto a cell complex of dimension equal to the virtual cohomological dimension of the mapping class group. The image of the deformation retraction is contained in the CW complex first described by Thurston – the Thurston spine. The Thurston spine is the set of points in Teichmüller space corresponding to hyperbolic surfaces for which the set of shortest geodesics (the systoles) cuts the surface into polygons.