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Lectures on representations of surface groups

Author: François Labourie
Publisher: Zurich, Switzerland : European Mathematical Society, [2013] ©2013
Series: Zurich lectures in advanced mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Details

Document Type: Book
All Authors / Contributors: François Labourie
ISBN: 9783037191279 3037191279
OCLC Number: 875295355
Description: vii, 138 pages : illustrations ; 24 cm.
Contents: 1. Introduction --
2. Surfaces --
3. Vector bundles and connections --
4. Twisted cohomology --
5. Moduli spaces --
6. Symplectic structure --
7. 3-manifolds and integrality questions.
Series Title: Zurich lectures in advanced mathematics.
Responsibility: François Labourie.

Abstract:

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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