5,147 research outputs found
On groups whose geodesic growth is polynomial
This note records some observations concerning geodesic growth functions. If
a nilpotent group is not virtually cyclic then it has exponential geodesic
growth with respect to all finite generating sets. On the other hand, if a
finitely generated group has an element whose normal closure is abelian and
of finite index, then has a finite generating set with respect to which the
geodesic growth is polynomial (this includes all virtually cyclic groups).Comment: 11 pages, 1 figur
Geodesic growth in virtually abelian groups
We show that the geodesic growth function of any finitely generated virtually
abelian group is either polynomial or exponential; and that the geodesic growth
series is holonomic, and rational in the polynomial growth case. In addition,
we show that the language of geodesics is blind multicounter.Comment: 23 pages, 1 figure, improved readabilit
Some geometric groups with rapid decay
We explain some simple methods to establish the property of Rapid Decay for a
number of groups arising geometrically. We also give new examples of groups
with the property of Rapid Decay. In particular we establish the property of
Rapid Decay for all lattices in rank one Lie groups.Comment: 30 pages, 0 figures. There is a change in the content of the paper.
The statement of Theorem 0.5 involving cube complexes in the original version
fo the paper was incorrect. There is a change in the content of the paper.
The proof of Lemma 2.10 needed the use of a result in Drutu-Sapir. This was
pointed out to us by D. Groves. The paper has been accepted by GAFA for
publicatio
- …