Lectures on representations of surface groups Francois Labourie

By:

Labourie, Francois

Series: Zurich lectures in advanced mathematics | Zurich lectures in advanced mathematicsDescription: vii, 138 p. ill. 24 cmISBN:

9783037191279
3037191279

Subject(s):

DDC classification:

512.482

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.

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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Item type	Current library	Call number	Copy number	Status	Date due	Barcode
Carti	IMAR	512.482-LAB (Browse shelf(Opens below))	1	Checked out	10/30/2025	0033947

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Previous	512.482-HIL Lie Groups, Convex Cones, and Semigroups	512.482-KAP Lie Algebras and locally compact groups	512.482-KUM Conformal Blocks Generalized Theta Function and the Verlinde Formula	512.482-LAB Lectures on representations of surface groups	512.482-MAC General Theory of Lie Groupoids and Lie Algebroids (London Mathematical Society Lecture Note Series, Series Number 213)	512.482-MAL Linear algebraic groups and finite groups of lie type	512.482-MAR An introduction to Kac-Moody groups over fields	Next

eng

Bibliografie
Index
System Control Number (OCoLC)ocn875295355

1. Introduction -- 2. Surfaces -- 3. Vector bundles and connections -- 4. Twisted cohomology -- 5. Moduli spaces -- 6. Symplectic structure -- 7. 3-manifolds and integrality questions.

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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