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SUMMARY: The geometry of Higman groups
DTSTART:20151119T130000
DTEND:20151119T140000
DTSTAMP:20260510T235144Z
UID:b8a02cb92c99fb9542e0fcb97f5eb5b0af3aad7d1b4ca46be374e3ce
CATEGORIES:Conferences - Seminars
DESCRIPTION:Alexandre Martin (Vienna)\nThe Higman group was constructed as
  the first example of a finitely\npresented infinite group without non-tri
 vial finite quotients. Despite\nthis pathological behaviour\, I will descr
 ibe striking similarities with\nmapping class groups of hyperbolic surface
 s\, outer automorphisms of free\ngroups and special linear groups over the
  integers. The main object of\nstudy will be the cocompact action of the g
 roup on a CAT(0) square complex\nnaturally associated to its standard pres
 entation. This action\, which\nturns out to be intrinsic\, can be used to 
 explicitly compute the\nautomorphism group of the Higman group\, and to sh
 ow that the group is both\nHopfian and co-Hopfian\, among other things.\nI
 f time allows\, I will also mention the action of generalised Higman\ngrou
 ps on associated CAT(-1) polygonal complexes\, and show that their\ndynami
 cal properties push the analogy with mapping class groups even\nfurther.
LOCATION:MA31 http://plan.epfl.ch/?room=ma31
STATUS:CONFIRMED
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