Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated groups.
Time and place
1 PM on Tuesday, March 16th, 2010; NAC 6113
Prof. Tullia Dymarz (Yale University)
Abstract
In geometric group theory we are interested in studying finitely
generated groups as geometric objects. A finitely generated group
can be considered as a metric space when endowed with a word
metric'. This word metric depends on the choice of generating set
but all such metrics are bilipschitz equivalent. Usually, however,
finitely generated groups are studied up toquasi-isometry'.
This is a coarse version of bilipschitz equivalence that allows one
to study these groups by studying proper geodesic metric spaces on
which they act. I will give examples that show that these two
notions are not equivalent. The proof will give a flavor of some of
the varied techniques and theorems currently used to study the
geometry of finitely generated groups.
