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163,40 ۥ Preface ix
• Remarks on Wilson Loops and Seifert Loops in Chern-Simons Theory 1
• Quantum Field Theory and the Volume Conjecture 19
• Computational Aspects in Reidemeister Torsion and Chern–Simons Theories 43
• Functional Integration and Abelian Link Invariants 65
• Chern-Simons Invariants, SO(3) Instantons, and Z/2 Homology Cobordism 83
• Extending the SU(3) Casson Invariant to Rational Homology 3-Spheres 115
• Decomposition of Witten–Reshetikhin–Turaev Invariant: Representations and the Colored Jones Polynomial of a Torus Knot 153
• Eta-Invariants and Anomalies in U(1) Chern-Simons Theory 173
• Delta-Groupoids and Ideal Triangulations 201
• Invariants of Knots and 3–Manifolds Derived from the Equivariant Linking Pairing 217
• Chern–Simons Theory, the 1/N Expansion, and String Theory 243
• Global Lorentzian Geometry from Lightlike Geodesics: What Does an Observer in (2+1)-Gravity See? 261
• Spin Foam State Sums and Chern-Simons Theory 277
• Representations of the Ptolemy Groupoid, Johnson Homomorphisms, and Finite Type Invariants 285
• Yang-Mills in Two Dimensions and Chern-Simons in Three 307
• Intersection Pairings on Spaces of Connections and Chern-Simons Theory on Seifert Manifolds 317
• Fermionization and Convergent Perturbation Expansions in Chern-Simons Gauge Theory 331
• Analytic Continuation of Chern-Simons Theory 347
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.
Authors
• Jørgen E. Andersen: Aarhus University, Aarhus, Denmark,
• Hans U. Boden: McMaster University, Hamilton, ON, Canada,
• Atle Hahn: Universidade de Lisboa, Lisboa, Portugal,
• Benjamin Himpel: Universität Bonn, Bonn, Germany
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