BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Junior Geometry Seminar
SUMMARY:A cubical Rips construction - Macarena Arenas\, Un
iversity of Cambridge
DTSTART;TZID=Europe/London:20220211T160000
DTEND;TZID=Europe/London:20220211T170000
UID:TALK168107AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/168107
DESCRIPTION:The Rips exact sequence is a useful tool for produ
cing examples of groups satisfying combinations of
properties that are not obviously compatible. It
works by taking as an input an arbitrary finitely
presented group Q\, and producing as an output a
hyperbolic group G that maps onto Q with finitely
generated kernel. The "output group" G is crafted
by adding generators and relations to a presentati
on of Q\, in such a way that these relations creat
e enough "noise" in the presentation to ensure hyp
erbolicity. One can then lift pathological propert
ies of Q to (some subgroup of) G. Among other thin
gs\, Rips used his construction to produce the fir
st examples of incoherent hyperbolic groups\, and
of hyperbolic groups with unsolvable generalised w
ord problem.\n \nIn this talk\, I will explain Rip
s’ result\, mention some of its variations\, and s
urvey some tools and concepts related to these con
structions\, including small cancellation theory\,
cubulated groups\, and asphericity. Time permitti
ng\, I will describe a variation of the Rips const
ruction that produces cubulated hyperbolic groups
of any desired cohomological dimension.\n
LOCATION:MR13
CONTACT:Macarena Arenas
END:VEVENT
END:VCALENDAR