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Softcover ISBN:  9780821853535 
Product Code:  AMSIP/50 
List Price:  $154.00 
MAA Member Price:  $138.60 
AMS Member Price:  $123.20 
eBook ISBN:  9781470417536 
Product Code:  AMSIP/50.E 
List Price:  $144.00 
MAA Member Price:  $129.60 
AMS Member Price:  $115.20 
Softcover ISBN:  9780821853535 
eBook ISBN:  9781470417536 
Product Code:  AMSIP/50.B 
List Price:  $298.00 $226.00 
MAA Member Price:  $268.20 $203.40 
AMS Member Price:  $238.40 $180.80 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 50; 2011; 446 ppMSC: Primary 11; 14; 16; 19; 20; 30; 32; 46; 53;
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 ChernSimons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them lowdimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory.
The 20year anniversary of Witten's discovery provided an opportunity to bring together researchers working in ChernSimons 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 ChernSimons gauge theory.ReadershipGraduate students and research mathematicians interested in mathematical physics; topological quantum field theory; ChernSimons theory.

Table of Contents

Chapters

Remarks on Wilson loops and Seifert loops in ChernSimons theory

Quantum field theory and the volume conjecture

Computational aspects in Reidemeister torsion and ChernSimons theories

Functional integration and abelian link invariants

ChernSimons invariants, SO(3) instantons, and $\mathbb {Z}/2$ homology cobordism

Extending the $SU(3)$ Casson invariant to rational homology 3spheres

Decomposition of WittenReshetikhinTuraev invariant: Linking pairing and modular forms

Representations and the colored Jones polynomial of a torus knot

Etainvariants and anomalies in $U/1$ ChernSimons theory

Deltagroupoids and ideal triangulations

Invariants of knots and 3manifolds derived from the equivariant linking pairing

ChernSimons theory, the $1/N$ expansion, and string theory

Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)gravity see?

Spin foam state sums and ChernSimons theory

Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants

YangMills in two dimensions and ChernSimons in three

Intersection pairings on spaces of connections and ChernSimons theory on Seifert manifolds

Fermionization and convergent perturbation expansions in ChernSimons gauge theory

Analytic continuation of ChernSimons theory


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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 ChernSimons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them lowdimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory.
The 20year anniversary of Witten's discovery provided an opportunity to bring together researchers working in ChernSimons 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 ChernSimons gauge theory.
Graduate students and research mathematicians interested in mathematical physics; topological quantum field theory; ChernSimons theory.

Chapters

Remarks on Wilson loops and Seifert loops in ChernSimons theory

Quantum field theory and the volume conjecture

Computational aspects in Reidemeister torsion and ChernSimons theories

Functional integration and abelian link invariants

ChernSimons invariants, SO(3) instantons, and $\mathbb {Z}/2$ homology cobordism

Extending the $SU(3)$ Casson invariant to rational homology 3spheres

Decomposition of WittenReshetikhinTuraev invariant: Linking pairing and modular forms

Representations and the colored Jones polynomial of a torus knot

Etainvariants and anomalies in $U/1$ ChernSimons theory

Deltagroupoids and ideal triangulations

Invariants of knots and 3manifolds derived from the equivariant linking pairing

ChernSimons theory, the $1/N$ expansion, and string theory

Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)gravity see?

Spin foam state sums and ChernSimons theory

Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants

YangMills in two dimensions and ChernSimons in three

Intersection pairings on spaces of connections and ChernSimons theory on Seifert manifolds

Fermionization and convergent perturbation expansions in ChernSimons gauge theory

Analytic continuation of ChernSimons theory