Geometric structures and representations of surface groups.
Thursday, 10 November, 2022 - 17:00
In the end of the 19th century, Klein introduced a notion of geometric structure on a manifold associated to a group action on a model space. This notion includes the notion of euclidean, hyperbolic structures, but also flat conformal and projective structures on manifolds.
We will consider some examples of geometric structures on surfaces and see how one can associate to such a structure a representation of a surface group. In particular the space of hyperbolic structures on a surface corresponds to a connected component of the space of representations of the correspongind surface groups.
Finally we will see that one can draw a similar picture for convex projective structures on a surface.
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