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DESCRIPTION: From Kalai's classic paper generalizing Cayley's tree-enumerat
ion formula to simplicial complexes\, it is known that simplicial complexes
on a small number of vertices can have enormous torsion in homology. Moreo
ver\, 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 su
ch complexes. In particular\, I will discuss my work to use the probabilist
ic method to construct optimally small (up to a constant factor from a know
n 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.
DTSTAMP:20181105T173500
DTSTART:20180604T141500
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n room MA 041 (ground floor)
SEQUENCE:0
SUMMARY:Andrew Newman (Ohio State University): Small simplicial complexes w
ith large torsion in homology
UID:89312371@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20180604-C-Newman.html
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