# Almost Commuting Elements in Compact Lie Groups (Memoirs of the American Mathematical Society No. 157)

By: John W. Morgan (author), Robert Friedman (author), Armand Borel (author)Paperback

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### Description

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 te' 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.

### Contents

Introduction Almost commuting $N$-tuples Some characterizations of groups of type $A$ $c$-pairs Commuting triples Some results on diagram automorphisms and associated root systems The fixed subgroup of an automorphism $C$-triples The tori $\overline{S}(k)$ and $\overline{S}^{w c}(\overline{\bf g}, k)$ and their Weyl groups The Chern-Simons invariant The case when $\langle C\rangle$ is not cyclic Bibliography Diagrams and tables.

### Product Details

• publication date: 15/03/2002
• ISBN13: 9780821827925
• Format: Paperback
• Number Of Pages: 136
• ID: 9780821827925
• weight: 283
• ISBN10: 0821827928

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