**Contemporary Mathematics**

Volume: 416;
2006;
284 pp;
Softcover

MSC: Primary 11; 57;

**Print ISBN: 978-0-8218-3456-5
Product Code: CONM/416**

List Price: $92.00

AMS Member Price: $73.60

MAA Member Price: $82.80

**Electronic ISBN: 978-0-8218-8095-1
Product Code: CONM/416.E**

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

# Primes and Knots

Share this page *Edited by *
*Toshitake Kohno; Masanori Morishita*

This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.

#### Readership

Graduate students and research mathematicians interested in low-dimensional topology, number theory, and relations between them.

# Table of Contents

## Primes and Knots

- Contents v6 free
- Preface vii8 free
- Categorification of the skein module of tangles 110 free
- The double shuffle relations for p-adic multiple zeta values 918
- Galois p-groups unramified at p - A survey 3140
- On capitulation theorems for infinite groups 4150
- Multiple zeta values and Grothendieck-Teichmüller groups 4958
- Asymptotics of q-difference equations 8392
- 1. Introduction 8493
- 1.1. The goal 8493
- 1.2. The colored Jones function 8493
- 1.3. The Hyperbolic Volume Conjecture 8594
- 1.4. q-difference equations 8695
- 1.5. Asymptotics of differential equations with a parameter 8695
- 1.6. Asymptotics of difference equations 8796
- 1.7. Asymptotics of difference equations with a parameter 8897
- 1.8. Statement of the results 91100
- 1.9. What's next? 91100
- 1.10. Acknowledgement 91100

- 2. є-difference equations 91100
- 3. Some linear algebra 95104
- 4. Existence of formal solutions 96105
- 5. Proof of Theorem 3 99108
- 6. Regular solutions and their asymptotics 107116
- 7. Applications to Quantum Topology 109118
- References 113122

- The mapping class group acts reducibly on SU(n)-character varieties 115124
- Pro-p link groups and p-homology groups 121130
- Introduction 121130
- 1. Pro-p completion of a link group 123132
- 2. p-adic Milnor invariants 125134
- 3. Completed Alexander modules 127136
- 4. Galois module structure of the p-homology group of a p-fold cyclic branched cover 130139
- 5. Iwasawa type formulas for the p-homology groups of pm-fold cyclic branched covers 133142

- A quantum introduction to knot theory 137146
- Classical knot invariants and elementary number theory 167176
- Harmonic and equianharmonic equations in the Grothendieck-Teichmüller group, II 197206
- On p-adic properties of the Witten-Reshetikhin-Turaev invariant 213222
- Seiberg-Witten integrable systems and periods of rational elliptic surfaces 237246
- On the finiteness of various Galois representations 249258
- Some new-type equations in the Grothendieck-Teichmüller group arising from geometry of Mo,5 263272