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Title: Foliated projective structures
and the Hitchin component for PSL(4,R)
Abstract: Around 1990 Hitchin proved that there is a connected component,
of the representation variety of the fundamental group of a closed surface
into PSL(n,R), which is homoemorphic to a ball. In many ways this Hitchin
component seems to be a "higher" analogue of Teichmueller space.
In this talk I will explain that the Hitchin component for PSL(4,R) can
be interpreted as the moduli space of special projective structures on
the unit tangent bundle of the surface. This gives a further analogy to
Teichmueller space. This is joint work with Olivier Guichard. |