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SUMMARY:Higher Teichmüller Spaces for Orbifolds
DTSTART;VALUE=DATE-TIME:20190506T143000Z
DTEND;VALUE=DATE-TIME:20190506T154500Z
DTSTAMP;VALUE=DATE-TIME:20200714T081254Z
UID:indico-event-4490@indico.math.cnrs.fr
DESCRIPTION:The Teichmüller space of a compact 2-orbifold X can be define
d as the space of faithful and discrete representations of the fundamental
group $\\pi_1$(X) of X into PGL(2\,R). It is a contractible space. For cl
osed orientable surfaces\, "higher analogues" of the Teichmüller space ar
e\, by definition\, (unions of) connected components of representation var
ieties of $\\pi_1$(X) that consist entirely of discrete and faithful repre
sentations. There are two known families of such spaces\, namely Hitchin r
epresentations and maximal representations\, and conjectures on how to fin
d others. In joint work with Daniele Alessandrini and Gye-Seon Lee\, we sh
ow that the natural generalisation of Hitchin components to the orbifold c
ase yields new examples of higher Teichmüller spaces: Hitchin representat
ions of orbifold fundamental groups are discrete and faithful\, and share
many other properties of Hitchin representations of surface groups. Howeve
r\, we also uncover new phenomena\, which are specific to the orbifold cas
e.\n\nhttps://indico.math.cnrs.fr/event/4490/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4490/
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