Online Talk

A Bier sphere is a deleted join of a simplicial complex different from a simplex and its Alexander dual complex. This simple and beautiful construction leads to a wide class of PL-spheres; almost all of them are non-polytopal when the number of vertices tends to infinity. In this talk, we will discuss two combinatorial invariants of Bier spheres
playing an important role in toric topology: the chromatic and Buchstaber numbers. Then we are going to construct a canonical regular realization for any Bier sphere and define the corresponding real and complex
canonical toric manifolds. Finally, we will talk about some corollaries of that construction, including a topological proof of the Dehn-Sommerville relations for Bier spheres.
 

The talk is based on joint works with Marinko Timotijevic, Ales Vavpetic, and Rade Zivaljevic.