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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Group actions on quasi-median graphs and acylindri
cal hyperbolicity - Motiejus Valiunas (Southampton
)
DTSTART;TZID=Europe/London:20190222T134500
DTEND;TZID=Europe/London:20190222T144500
UID:TALK118762AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/118762
DESCRIPTION:CAT (0) cube complexes form a class of non-positiv
ely curved spaces playing a special role in geomet
ric group theory. For instance\, such spaces arise
naturally in the study of right-angled Artin or C
oxeter groups. These complexes can be identified w
ith the class of median graphs\, and the latter ca
n be generalised to quasi-median graphs\, or 'CAT
(0) prism complexes'. Recent work of A. Genevois h
as equipped quasi-median graphs with a rich combin
atorial structure akin to that of CAT (0) cube com
plexes\, which is useful in studying group actions
. In particular\, we may use quasi-median graphs t
o study graph products - a class of groups that in
terpolate between direct and free products.\n\nIn
this talk I will give a brief introduction to quas
i-median graphs and their cubical-like geometry. I
will construct the 'contact graph' of a quasi-med
ian graph\, which turns out to be quasi-isometric
to a tree\, and explain the conditions under which
a group action on a quasi-median graph induces a
particularly nice (acylindrical) action on the con
tact graph. If time permits\, I will outline an ap
plication or two to graph products.
LOCATION:CMS\, MR13
CONTACT:Richard Webb
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