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SUMMARY:Domains of discontinuity for (quasi-)Hitchin representations
DTSTART;VALUE=DATE-TIME:20180425T143000Z
DTEND;VALUE=DATE-TIME:20180425T154500Z
DTSTAMP;VALUE=DATE-TIME:20210508T080759Z
UID:indico-event-3432@indico.math.cnrs.fr
DESCRIPTION:Among representations of surface groups into Lie groups\, the
Anosov representations are the ones with the nicest dynamical properties.
\n\nGuichard-Wienhard and Kapovich-Leeb-Porti have shown that their action
s on generalized flag manifolds often admit co-compact domains of disconti
nuity\, whose quotients are closed manifolds carrying interesting geometri
c structures. \n\nDumas and Sanders studied the topology and the geometry
of the quotient in the case of quasi-Hitchin representations (Anosov repre
sentations which are deformations of Hitchin representations). In a conjec
ture they ask whether these manifolds are homeomorphic to fiber bundles ov
er the surface. \n\nIn joint work with Qiongling Li\, we can prove that th
e conjecture is true for (quasi-)Hitchin representations in SL(n\,R) and S
L(n\,C)\, acting on projective spaces and partial flag manifolds parametri
zing points and hyperplanes.\n\nhttps://indico.math.cnrs.fr/event/3432/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3432/
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