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Lectures on Representations of Surface Groups
Zurich Lectures in Advanced Mathematics

François Labourie (Université Paris Sud, Orsay, France)

Lectures on Representations of Surface Groups

ISBN print 978-3-03719-127-9, ISBN online 978-3-03719-627-4
DOI 10.4171/127
December 2013, 145 pages, softcover, 17 x 24 cm.
32.00 Euro

The subject of these notes is the character variety of representations of a surface group in a Lie group. We emphasize the various points of view (combinatorial, differential, algebraic) and are interested in the description of its smooth points, symplectic structure, volume and connected components. We also show how a three manifold bounded by the surface leaves a trace in this character variety.

These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In the first chapters, we do not insist in the details of the differential geometric constructions and refer to classical textbooks, while in the more advanced chapters proofs occasionally are provided only for special cases where they convey the flavor of the general arguments. These notes could also be used by researchers entering this fast expanding field as motivation for further studies proposed in a concluding paragraph of every chapter.

Keywords: Surface groups, symplectic geometry, Lie groups, character variety

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