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SUMMARY:Profinite completions\, curvature\, and decision problems - Martin
  Bridson (Oxford)
DTSTART:20111116T141500Z
DTEND:20111116T151500Z
UID:TALK34202@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:In 1970 Grothendieck asked: if G_1 and G_2 are finitely\nprese
 nted\, residually finite groups\, and there is a map between them that\nin
 duces an isomorphism of profinite completions\, must the original map be a
 n\nisomorphism? Fritz Grunewald  and I showed that the answer is "no". Our
 \nsolution opens up a rich array of possibilities around the questions: ho
 w\ndifferent can G_1 and G_2 be? and what additional hypotheses force G_1 
 to\nbe isomorphic to G_2?  I shall describe recent progress on these quest
 ions\,\nexplaining in particular how dramatically the algorithmic complexi
 ty of G_1\nand G_2 can differ.
LOCATION:MR13\, CMS
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