Lectures on representations of surface groups
by François Labourie
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. --
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Lie groups, Differential Geometry, Topological groups, Groupes de Lie, Géométrie différentielle, Groupes topologiques, Differential & Riemannian geometry, MATHEMATICS, Algebra, Intermediate, Differential geometry, Several complex variables and analytic spaces, Global analysis, analysis on manifolds| Edition | Availability |
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Lectures on representations of surface groups
2013, European Mathematical Society
in English
3037191279 9783037191279
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Includes bibliographical references (pages 132-135) and index.
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| December 11, 2022 | Edited by MARC Bot | import existing book |
| November 14, 2020 | Created by MARC Bot | import new book |