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SUMMARY:Presentations for Brin’s higher-dimensional Thompson groups nV -
  Martyn Quick (St Andrews)
DTSTART:20191204T163000Z
DTEND:20191204T173000Z
UID:TALK134062@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:In 2004\, Brin introduced\, for each integer n >= 2\, a group 
 nV consisting of certain\nhomeomorphisms of n-dimensional Cantor space. Th
 is generalises the group V defined by Richard Thompson in\n1965 and provid
 es further examples of finitely presented infinite simple groups.  In thi
 s talk\, I will\ndescribe recent work that gives new presentations for eac
 h of the groups nV obtained by exploiting\ntranspositions of disjoint basi
 c open sets.  The first presentation is infinite\, is analogous to the\nC
 oxeter presentation for the finite symmetric group and reflects the self-s
 imilar structure of Cantor\nspace.  The second is a reduction to a finite
  presentation that is considerably smaller than those\npreviously known.
LOCATION:MR12
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