Geometry vs. Topology: On 4-Polytopes and 3-Spheres

Date

Jan 25, 2017

Time

5:00 PM - 6:00 PM

Speaker

Prof. Günter M. Ziegler

Affiliation

Dresdner Mathematisches Seminar Prof. Günter M. Ziegler Freie Universität Berlin, FB Mathematik und Informatik, Arbeitsgruppe Diskrete Geometrie

Series

TUD Dresdner Mathematisches Seminar

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. A. Thom

Description

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: The sets of f-vectors of 3-spheres and of 4-polytopes do not coincide. (Joint work with Philip Brinkmann)

Last modified: Jan 19, 2017, 11:28:33 AM