Presented by:
Anthony Genevois
Date:
Tuesday 10th January 2017 - 14:30 to 15:30
Venue:
INI Seminar Room 1
Abstract:
In 1994, Bandelt, Mulder and Wilkeit introduced a class of graphs
generalizing the so-called median graphs: the class of quasi-median
graphs. Since the works of Roller and Chepoï, we know that median graphs
and CAT(0) cube complexes essentially define the same objets, and
because CAT(0) cube complexes play an important role in recent reseach
in geometric group theory, a natural question is whether quasi-median
graphs can be used to study some classes of groups. In our talk, we will
show that quasi-median graphs and CAT(0) cube complexes share
essentially the same geometry. Moreover, extending the observation that
right-angled Artin and Coxeter groups have a Cayley graph which is
median, arbitrary graph products turn out to have a Cayley graph (with
respect to a natural, but possibly infinite, generating set) which is
quasi-median. The main goal of this talk is to show how to use the
quasi-median geometry of this Cayley graph to study graph products.
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