Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Almost Commuting Elements in Compact Lie Groups
 
Armand Borel Institute for Advanced Study, Princeton, NJ
Robert Friedman Columbia University, New York, NY
John W. Morgan Columbia University, New York City, NY
Front Cover for Almost Commuting Elements in Compact Lie Groups
Available Formats:
Electronic ISBN: 978-1-4704-0340-9
Product Code: MEMO/157/747.E
136 pp 
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
Front Cover for Almost Commuting Elements in Compact Lie Groups
Click above image for expanded view
  • Front Cover for Almost Commuting Elements in Compact Lie Groups
  • Back Cover for Almost Commuting Elements in Compact Lie Groups
Almost Commuting Elements in Compact Lie Groups
Armand Borel Institute for Advanced Study, Princeton, NJ
Robert Friedman Columbia University, New York, NY
John W. Morgan Columbia University, New York City, NY
Available Formats:
Electronic ISBN:  978-1-4704-0340-9
Product Code:  MEMO/157/747.E
136 pp 
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1572002
    MSC: Primary 22; 17; Secondary 57;

    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.

    Readership

    Graduate students and research mathematicians interested in topological groups, Lie groups, and nonassociative rings and algebras.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Almost commuting $N$-tuples
    • 3. Some characterizations of groups of type $A$
    • 4. $c$-pairs
    • 5. Commuting triples
    • 6. Some results on diagram automorphisms and associated root systems
    • 7. The fixed subgroup of an automorphism
    • 8. $C$-triples
    • 9. The tori $\bar {S}(k)$ and $\bar {S}^{w_C}(\bar {\mathbf {g}},k)$ and their Weyl groups
    • 10. The Chern-Simons invariant
    • 11. The case when $\langle C\rangle $ is not cyclic
  • Request Review Copy
  • Get Permissions
Volume: 1572002
MSC: Primary 22; 17; Secondary 57;

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.

Readership

Graduate students and research mathematicians interested in topological groups, Lie groups, and nonassociative rings and algebras.

  • Chapters
  • 1. Introduction
  • 2. Almost commuting $N$-tuples
  • 3. Some characterizations of groups of type $A$
  • 4. $c$-pairs
  • 5. Commuting triples
  • 6. Some results on diagram automorphisms and associated root systems
  • 7. The fixed subgroup of an automorphism
  • 8. $C$-triples
  • 9. The tori $\bar {S}(k)$ and $\bar {S}^{w_C}(\bar {\mathbf {g}},k)$ and their Weyl groups
  • 10. The Chern-Simons invariant
  • 11. The case when $\langle C\rangle $ is not cyclic
Please select which format for which you are requesting permissions.