**Contemporary Mathematics**

Volume: 541;
2011;
257 pp;
Softcover

MSC: Primary 57; 32; 60; 16; 17; 81; 11; 14;

Print ISBN: 978-0-8218-4960-6

Product Code: CONM/541

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

**Electronic ISBN: 978-0-8218-8220-7
Product Code: CONM/541.E**

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

# Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory

Share this page *Edited by *
*Abhijit Champanerkar; Oliver Dasbach; Efstratia Kalfagianni; Ilya Kofman; Walter Neumann; Neal Stoltzfus*

This book is based on a 10-day workshop given by leading experts in
hyperbolic geometry, quantum topology and number theory, in June 2009 at
Columbia University. Each speaker gave a minicourse consisting of three or
four lectures aimed at graduate students and recent PhDs. The proceedings of
this enormously successful workshop can serve as an introduction to this
active research area in a way that is expository and broadly accessible to
graduate students.

Although many ideas overlap, the twelve expository/research papers in this
volume can be grouped into four rough categories:

(1) different approaches to the Volume Conjecture, and relations
between the main quantum and geometric invariants;

(2) the geometry associated to triangulations of hyperbolic 3-manifolds;

(3) arithmetic invariants of hyperbolic 3-manifolds;

(4) quantum invariants associated to knots and hyperbolic
3-manifolds.

The workshop, the conference that followed, and these proceedings
continue a long tradition in quantum and geometric topology of
bringing together ideas from diverse areas of mathematics and physics,
and highlights the importance of collaborative research in tackling
big problems that require expertise in disparate
disciplines.

#### Readership

Graduate students and research mathematicians interested in hyperbolic geometry, quantum topology and number theory.

# Table of Contents

## Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory

- Contents vii8 free
- Preface ix10 free
- List of Participants xi12 free
- An Introduction to the Volume Conjecture 116 free
- Quantum Field Theory and the Volume Conjecture 4156
- R-Matrix Knot Invariants and Triangulations 6984
- Knots and Tropical Curves 8398
- Quantum Coadjoint Action and the 6j-Symbols of Uqsl2 103118
- What is a Sequence of Nilsson Type? 145160
- From Angled Triangulations to Hyperbolic Structures 159174
- Triangulated 3-Manifolds: From Haken's Normal Surfaces to Thurston's Algebraic Equation 183198
- An Introduction to Fully Augmented Links 205220
- Orbifolds and Commensurability 221236
- Realizing Arithmetic Invariants of Hyperbolic 3-Manifolds 233248
- Fields of Definition of Canonical Curves 247262