**AMS/IP Studies in Advanced Mathematics**

Volume: 50;
2011;
446 pp;
Softcover

MSC: Primary 11; 14; 16; 19; 20; 30; 32; 46; 53; 54; 55; 57; 58; 70; 81; 83;

Print ISBN: 978-0-8218-5353-5

Product Code: AMSIP/50

List Price: $137.00

Individual Member Price: $109.60

**Electronic ISBN: 978-1-4704-1753-6
Product Code: AMSIP/50.E**

List Price: $137.00

Individual Member Price: $109.60

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# Chern-Simons Gauge Theory: 20 Years After

Share this page *Edited by *
*Jørgen E. Andersen; Hans U. Boden; Atle Hahn; Benjamin Himpel*

A co-publication of the AMS and International Press of Boston, Inc.

In 1989, Edward Witten discovered a deep
relationship between quantum field theory and knot theory, and this
beautiful discovery created a new field of research called
Chern-Simons theory. This field has the remarkable feature of
intertwining a large number of diverse branches of research in
mathematics and physics, among them low-dimensional topology,
differential geometry, quantum algebra, functional and stochastic
analysis, quantum gravity, and string theory.

The 20-year anniversary of Witten's discovery provided an
opportunity to bring together researchers working in Chern-Simons
theory for a meeting, and the resulting conference, which took place
during the summer of 2009 at the Max Planck Institute for Mathematics
in Bonn, included many of the leading experts in the field. This
volume documents the activities of the conference and presents several
original research articles, including another monumental paper by
Witten that is sure to stimulate further activity in this and related
fields. This collection will provide an excellent overview of the
current research directions and recent progress in Chern-Simons gauge
theory.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

#### Readership

Graduate students and research mathematicians interested in mathematical physics; topological quantum field theory; Chern-Simons theory.

# Table of Contents

## Chern-Simons Gauge Theory: 20 Years After

- Cover Cover11
- Title page iii4
- Contents v6
- Frontispiece vii8
- Preface ix10
- List of speakers xi12
- List of participants xiii14
- Remarks on Wilson loops and Seifert loops in Chern-Simons theory 116
- Quantum field theory and the volume conjecture 1934
- Computational aspects in Reidemeister torsion and Chern-Simons theories 4358
- Functional integration and abelian link invariants 6580
- Chern-Simons invariants, SO(3) instantons, and ℤ/2 homology cobordism 8398
- Extending the 𝑆𝑈(3) Casson invariant to rational homology 3-spheres 115130
- Decomposition of Witten-Reshetikhin-Turaev invariant: Linking pairing and modular forms 131146
- Representations and the colored Jones polynomial of a torus knot 153168
- Eta-invariants and anomalies in 𝑈/1 Chern-Simons theory 173188
- Delta-groupoids and ideal triangulations 201216
- Invariants of knots and 3-manifolds derived from the equivariant linking pairing 217232
- Chern-Simons theory, the 1/𝑁 expansion, and string theory 243258
- Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)-gravity see? 261276
- Spin foam state sums and Chern-Simons theory 277292
- Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants 285300
- Yang-Mills in two dimensions and Chern-Simons in three 307322
- Intersection pairings on spaces of connections and Chern-Simons theory on Seifert manifolds 317332
- Fermionization and convergent perturbation expansions in Chern-Simons gauge theory 331346
- Analytic continuation of Chern-Simons theory 347362
- Back Cover Back Cover1466