Julien Marche
Published 2010-01-14Version 1
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.
Comments: 47 pages, 8 figures
The quantum $\mathfrak{sl}(n,\mathbb{C})$ representation theory and its applications
Categorification of invariants in gauge theory and sypmplectic geometry
On the existence of representations of finitely presented groups in compact Lie groups
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