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SUMMARY:When the outer automorphism groups of RAAGs are vast - Andrew Sale
  (Vanderbilt University)
DTSTART:20170112T160000Z
DTEND:20170112T170000Z
UID:TALK69896@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The outer  automorphism groups of right-angled Artin groups (R
 AAGs) give a way to build a bridge between GL(n\,Z) and  Out(Fn). We will 
 investigate certain properties of these  groups which could be described a
 s "vastness" properties\, and ask if it  possible to build a boundary betw
 een those which are "vast" and those  which are not.  One such property is
  as follows: given a group G\, we say G has all  finite groups involved if
  for each finite group H there is a finite  index subgroup of G which admi
 ts a map onto H. From the subgroup  congruence property\, it is known that
  the groups GL(n\,Z) do not have  every finite group involved for n>2. Mea
 nwhile\, the representations  of Out(Fn) given by Grunewald and Lubotzky i
 mply that these  groups do have all finite groups involved. We will descri
 be conditions  on the defining graph of a RAAG that are necessary and suff
 icient to  determine when it&#39\;s outer automorphism group has this prop
 erty. The same  criterion also holds for other properties\, such as SQ-uni
 versality\, or  having a finite index subgroup with infinite dimensional s
 econd bounded  cohomology. This is joint work with V. Guirardel. <br>
LOCATION:Seminar Room 1\, Newton Institute
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