Filling inequalities for nilpotent groups

Vendredi 19 octobre 2007 10:30-11:30 - Young Robert - Chicago et IHES

Résumé : I will give methods for bounding the higher-order filling functions of a homogeneous nilpotent group by constructing horizontal discs. Using these, I will construct examples of groups with arbitrarily large nilpotency class and quadratic Dehn functions.
The idea behind these methods is that some nilpotent groups have a scaling automorphism which expands some directions more than others.
Horizontal discs grow slowly when scaled, so fillings by such discs lead to filling inequalities. Gromov used horizontal discs to bound two-dimensional filling functions ; he used microflexibility to construct a compact family of horizontal discs and filled curves with scalings of those discs. I will extend this technique to higher dimensional fillings and show that in the case that the Lie group contains a lattice, it suffices to construct finitely many discs.

Lieu : bât. 425 - 225-227

Filling inequalities for nilpotent groups  Version PDF