AbstractThe classification of manifolds in various categories is a classical problem in topology. It has been widely investigated by applying techniques from geometric topology in the last century. However, the known results tell us very little information about the homotopy of manifolds. In the last ten years, there have been attempts to study the homotopy properties of manifolds by using tech...
AbstractIn this talk, we will introduce the canonical cell decomposition of Teichmuller space established by Ushijima, and compare the face relations to our own work on discrete conformal mapping. Then we will calculate several generalized Ptolemy equations on a hyperbolic surface. Finally, we will discuss some open problems on parameterization of Teichmuller space in order to make the face rel...
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