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SUMMARY:Moduli of Symplectic Maximal Representations - Guichard\, O (Paris
 -Sud 11 )
DTSTART:20110222T100000Z
DTEND:20110222T110000Z
UID:TALK30003@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Maximal representations of surface groups into symplectic real
  groups have been extensively studied in the last years. Beautiful results
  have been obtained using either the algebraic approach offered by the the
 ory of Higgs bundles or a geometric approach based on a formula coming fro
 m bounded cohomology.  \nAfter having recalled those results\, we will con
 struct\, for a maximal representation $\nho: pi_1(Sigma_g) 	o mathrm{Sp}(2
 n\, mathbf{R})$\, an open subset $Omega  ubset mathbf{R} mathbb{P}^{2n-1}$
  where $pi_1( Sigma_g)$ acts properly with compact quotient. The topology 
 of the quotient will then be determined.  \nFinally we shall consider the 
 problem of giving an interpretation of the moduli of maximal symplectic re
 presentations as a moduli space of $mathbf{R} mathbb{P}^{2n-1}$-structures
  and what are the questions that remain to give a complete answer to that 
 problem.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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