Almost Commuting Elements in Compact Lie Groups
Author: Armand Borel
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 153
ISBN-13: 0821827928
DOWNLOAD EBOOK →This text describes 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 the extended Dynkin diagram of the simply connected cover, together with the co-root 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.