Günter M. Ziegler (FU Berlin): Geometry vs. Topology: On 4-Polytopes and 3-Spheres

There has been massive efforts to understand the parameter spaces of convex polytopes -- and great results such as the “g-Theorem” were achieved on the way. On the other hand, key questions are still open, already and in particular for the case of 4-dimensional polytopes/3-dimensional spheres. One crucial question is “fatness problem” for 4-dimensional polytopes, which is a key to the question whether we should expect the same answers for convex polytopes (which are discrete-geometric objects) and for cellular spheres (a topological model), at least asymptotically. I will argue that we should not, and present first results in this direction.