From Kalai's classic paper generalizing Cayley's tree-enumeration formula to simplicial complexes, it is known that simplicial complexes on a small number of vertices can have enormous torsion in homology. Moreover, in a random setting one may find instances of this phenomenon such as, for example, a 3-dimensional simplicial complex on 30 vertices with the torsion subgroup of the second homology group having order larger than 10^^{82}. In this talk I will discuss the problem of explicitly constructing such complexes. In particular, I will discuss my work to use the probabilistic method to construct optimally small (up to a constant factor from a known lower bound) simplicial complexes with *prescribed* torsion in homology. I will also discuss an application of this work to the problem of counting homotopy types of simplicial complexes.

Jun 04, 2018 | 02:15 PM

Technische Universität Berlin

Institut für Mathematik

Straße des 17. Juni 136

10623 Berlin

room MA 041 (ground floor)

Campus map