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Memoirs of the American Mathematical Society
2002; 136 pp; softcover
List Price: US$65
Individual Members: US$39
Institutional Members: US$52
Order Code: MEMO/157/747
We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with the coroot integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
Graduate students and research mathematicians interested in topological groups, Lie groups, and nonassociative rings and algebras.
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