Primes and knots / Toshitake Kohno, Masanori Morishita, editors.

Format:

Book

Conference/Event

Contributor:

Kohno, Toshitake, editor.

Morishita, Masanori, 1961- editor.

Japan-U.S. Mathematics Institute, contributor.

Conference Name:

AMS Special Session on Primes and Knots (2003 : Baltimore Maryland), issuing body.

JAMI (Japan-U.S. Mathematics Institute) Conference (15th : 2003 : Johns Hopkins University, Baltimore, Maryland), issuing body.

Series:

Contemporary mathematics (American Mathematical Society) ; v. 416.

Contemporary mathematics, 0271-4132 ; volume 416

Language:

English

Subjects (All):

Algebraic number theory--Congresses.

Algebraic number theory.

Low-dimensional topology--Congresses.

Low-dimensional topology.

Physical Description:

1 online resource (298 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

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.

Contents:

""1.6. Asymptotics of difference equations""""1.7. 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 degree""""5.3. 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 varieties""""Pro-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""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8095-0