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SUMMARY:Higher Teichmueller theory: from PSL(2\,R) to other Lie groups - M
 arc Burger\, ETH
DTSTART:20170315T160000Z
DTEND:20170315T170000Z
UID:TALK70593@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:This is the first of four Leverhulme lectures on ``Higher Teic
 hmueller theory"\, whose  aim is to single out connected components of the
  G-representation variety of the fundamental group of a compact surface S 
 which are formed of representations with geometric significance.\n\nFor G 
 = PSl(2\,R) the component of interest\, Teichmueller space\, is formed by 
 all holonomy representations of hyperbolic structures on S. We'll describe
  two characterizations of Teichmueller space\, one by Fenchel Nielsen coor
 dinates which for G = PSl(n\,R) leads to the Hitchin component\, and the o
 ther by the maximality of the Euler number which for G = Sp(2n\,R) leads t
 o the components formed by maximal representations. From the point of view
  of geometric group theory\, in all cases these representations give rise 
 to quasi-isometric embeddings and this connection is provided by the conce
 pt of Anosov representation.\n
LOCATION:MR13
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