Lectures on representations of surface groups
By: François Labourie
Series: Zurich lectures in advanced mathematics; Zurich lectures in advanced mathematics
Publisher: European Mathematical Society
Published: 2013
Place of publication: Zürich, Switzerland
Language: eng
Number of pages: 138
ISBN-13: 9783037191279
Copyright date: 2013
Subjects: Lie groups; Differential Geometry; Topological groups
Description: 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. --
Notes: Includes bibliographical references (pages 132-135) and index.
Table of contents: title: 1. Introduction; title: 2. Surfaces; title: 3. Vector bundles and connections; title: 4. Twisted cohomology; title: 5. Moduli spaces; title: 6. Symplectic structure; title: 7. 3-manifolds and integrality questions.