Primes and Knots.

Primes and Knots.

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Bibliographic Details
Main Author: Kohno, Toshitake
Corporate Author: Japan-U.S. Mathematics Institute (Content Provider.)
Other Authors: Morishita, Masanori
Format: eBook
Language:English
Published: Providence : American Mathematical Society, 2006.
Series:Contemporary Mathematics.
Subjects:
Algebraic number theory > Congresses.
Low-dimensional topology > Congresses.
Algebraic number theory
Low-dimensional topology
Conference papers and proceedings
Online Access:Click for online access
Table of Contents:
  • 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

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