The Asymptotic Dimension of Box Spaces for Elementary Amenable Groups

arxiv: 1508.05018 · v1 · pith:EDGET25Anew · submitted 2015-08-20 · 🧮 math.MG · math.GR· math.GT

The Asymptotic Dimension of Box Spaces for Elementary Amenable Groups

Martin Finn-Sell , Jianchao Wu This is my paper

classification 🧮 math.MG math.GRmath.GT

keywords groupsasymptoticdimensionspacesamenableelementaryaboveadditively

0 comments p. Extension

pith:EDGET25A Add to your LaTeX paper

What is a Pith Number?

\usepackage{pith}
\pithnumber{EDGET25A}

Prints a linked pith:EDGET25A badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more

read the original abstract

We show that the asymptotic dimension of box spaces behaves (sub)additively with respect to extensions of groups. As a result, we obtain that for an elementary amenable group, the asymptotic dimension of any of its box spaces is bounded above by its Hirsch length. This bound is shown to be an equality for a large subclass of groups including all virtually polycyclic groups.

This paper has not been read by Pith yet.

The Asymptotic Dimension of Box Spaces for Elementary Amenable Groups

discussion (0)