Geometry of representation spaces in SU(2)

2010/01/14 by Julien Marché, Marche, Julien
Mathematics · Medicine · Physics and Astronomy · #37E30 #57M27 #57M50 #57M56 #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1001.2408

openalex publication_date 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly \su. We give detailed examples, develop the techniques of twisted cohomology and gauge theory. We review Chern-Simons theory and describe an integrable system for the representation space of a surface. Finally, we explain some basic ideas on geometric quantization. We apply them to the case of representation spaces by computing Bohr-Sommerfeld orbits with metaplectic correction.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

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