A quasi-regular cell complex is defined and shown to have a reasonable barycentric subdivision. In this setting, Whitney's theorem that the ^-skeleton of the barycentric subdivision of a triangulated n-manifold is dual to the (n-/c)th Stiefel-Whitney cohomology class is proven, and applied to projective spaces, lens spaces and surfaces. 1. QR complexes. A… (More)
We prove that in many, perhaps all, torsion free hyperbolic groups, test elements are precisely those elements not contained in proper retracts. We also show that all Fuchsian groups have this property. Finally, we show that all surface groups except Z × Z have test elements.