Contents -- Preface -- Categorification of the skein module of tangles -- The double shuffle relations for p-adic multiple zeta values -- Galois p-groups unramified at p -- A survey -- On capitulation theorems for infinite groups -- Multiple zeta values and Grothendieck-TeichmÃ?ller groups -- Asymptotics of q-difference equations -- 1. Introduction -- 1.1. The goal -- 1.2. The colored Jones function -- 1.3. The Hyperbolic Volume Conjecture -- 1.4. q-difference equations -- 1.5. Asymptotics of differential equations with a parameter
1.6. Asymptotics of difference equations1.7. Asymptotics of difference equations with a parameter -- 1.8. Statement of the results -- 1.9. What's next? -- 1.10. Acknowledgement -- 2. Ñ?-difference equations -- 2.1. Ñ?-difference equations -- 2.2. Converting q-difference equations to Ñ?-difference equations -- 3. Some linear algebra -- 4. Existence of formal solutions -- 4.1. An alternative formal series -- 5. Proof of Theorem 3 -- 5.1. Existence of a solution corresponding to the eigenvalue of maximum magnitude
5.2. A reduction to an Ñ?-difference equation of smaller degree5.3. The solutions form a locally fundamental set -- 6. Regular solutions and their asymptotics -- 6.1. Regular solutions to Ñ?-difference equations -- 6.2. Asymptotics of regular solutions of Ñ?-difference equations -- 6.3. Asymptotics of regular solutions of q-difference equations -- 7. Applications to Quantum Topology -- 7.1. The A-polynomial of a knot and its noncommutative version -- 7.2. Examples: The 31 and 41 knots -- References
The mapping class group acts reducibly on SU(n)-character varietiesPro-p link groups and p-homology groups -- Introduction -- 1. Pro-p completion of a link group -- 2. p-adic Milnor invariants -- 3. Completed Alexander modules -- 4. Galois module structure of the p-homology group of a p-fold cyclic branched cover -- 5. Iwasawa type formulas for the p-homology groups of pm-fold cyclic branched covers -- A quantum introduction to knot theory -- Classical knot invariants and elementary number theory
Harmonic and equianharmonic equations in the Grothendieck-TeichmÃ?ller group, IIOn p-adic properties of the Witten-Reshetikhin-Turaev invariant -- Seiberg-Witten integrable systems and periods of rational elliptic surfaces -- On the finiteness of various Galois representations -- Some new-type equations in the Grothendieck-TeichmÃ?ller group arising from geometry of Mo,5
