2014 - T1 - WS1 - Asymptotic properties of groups

Collection 2014 - T1 - WS1 - Asymptotic properties of groups

Organizer(s) Breuillard, Emmanuel ; Chatterji, Indira ; Erschler, Anna

Date(s) 24/03/2014 - 28/03/2014

linked URL https://web.archive.org/web/20220123001204/https://sites.google.com/site/geowalks2014/home/workshop

00:00:00 / 00:00:00

8 21

Imbeddings in groups of subexponential growth

By Laurent Bartholdi

A finitely generated group has subexponential growth if the number of group elements expressible as words of length $\le n$ growssubexponentially in $n$. I will show that every countable group that does not contain asubgroup of exponential growth imbeds in a finitely generated group ofsubexponential growth. This shows that there are no restrictions on being a subgroup of a group of exponential growth, except the obvious ones. This produces in particular the first examples of groups ofsubexponential growth containing $\mathbb Q$. This also producesgroups of subexponential growth and arbitrarily large distortion in uniformly convex Banach (e. g. \ Hilbert) spaces. This is joint work with Anna Erschler.

Information about the video

Date of publication 14/04/2014
Institution IHP
Licence CC BY-NC-ND
Format MP4

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