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Colloquium by Andrew Newman (Ohio State University): Small simplicial complexes with large torsion in homology

Jun 04, 2018 | 02:15 PM

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. 

Time & Location

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

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)