Low Dimensional Topology and Number Theory
Fukuoka, Japan, March 15?18, 2022. In Memory of Professor Toshie Takata
Series: Springer Proceedings in Mathematics & Statistics; 456;
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Product details:
- Edition number 2024
- Publisher Springer
- Date of Publication 2 March 2025
- Number of Volumes 1 pieces, Book
- ISBN 9789819737772
- Binding Hardback
- No. of pages379 pages
- Size 235x155 mm
- Language English
- Illustrations 50 Illustrations, black & white; 21 Illustrations, color 692
Categories
Short description:
This book is the result of research initiatives formed during the workshop "Low Dimensional Topology and Number Theory XIII" at Kyushu University in 2022. It is also dedicated to the memory of Professor Toshie Takata, who has been a main figure of the session chairs for the series of annual workshops since 2009.
The activity was aimed at understanding and deepening recent developments of lively and fruitful interactions between low-dimensional topology and number theory over the past decades.
In this volume of proceedings, the reader will find research papers as well as survey articles, including open problems, at the interface between classical and quantum topology, and algebraic and analytic number theory, written by leading experts and active researchers in the respective fields.
Topics include, among others, the strong slope conjecture; Kashiwara?Vergne Lie algebra; braids and ?bered double branched covers of 3-manifolds; Temperley?Lieb?Jones category and conformal blocks; WRT invariants and false theta functions; the colored Jones polynomial of the ?gure-eight knot; potential functions and A-polynomials; l-adic Galois polylogarithms; Dijkgraaf?Witten invariants in Bloch groups; analogies between knots and primes in arithmetic topology; normalized Jones polynomials for rational links; Iwasawa main conjecture; Weber?s class number problem.
The book provides a valuable resource for researchers and graduate students interested in topics related to both low-dimensional topology and number theory.
Long description:
This book is the result of research initiatives formed during the workshop "Low Dimensional Topology and Number Theory XIII" at Kyushu University in 2022. It is also dedicated to the memory of Professor Toshie Takata, who has been a main figure of the session chairs for the series of annual workshops since 2009.
The activity was aimed at understanding and deepening recent developments of lively and fruitful interactions between low-dimensional topology and number theory over the past decades.
In this volume of proceedings, the reader will find research papers as well as survey articles, including open problems, at the interface between classical and quantum topology, and algebraic and analytic number theory, written by leading experts and active researchers in the respective fields.
Topics include, among others, the strong slope conjecture; Kashiwara?Vergne Lie algebra; braids and ?bered double branched covers of 3-manifolds; Temperley?Lieb?Jones category andconformal blocks; WRT invariants and false theta functions; the colored Jones polynomial of the ?gure-eight knot; potential functions and A-polynomials; l-adic Galois polylogarithms; Dijkgraaf?Witten invariants in Bloch groups; analogies between knots and primes in arithmetic topology; normalized Jones polynomials for rational links; Iwasawa main conjecture; Weber?s class number problem.
The book provides a valuable resource for researchers and graduate students interested in topics related to both low-dimensional topology and number theory.
Table of Contents:
K. L. Baker, K. Motegi and T. Takata, The Strong Slope Conjecture and crossing numbers for Mazur doubles of knots.- H. Furusho and N. Komiyama, Notes on Kashiwara-Vergne and double shuffle Lie algebras.- S. Hirose and E. Kin, Braids, entropies and fibered 2-fold branched covers of 3-manifolds.- T. Kohno, Homological representations of braid groups at roots of unity and the space of conformal blocks.- T. Matsusaka, Hikami?s observations on unified WRT invariants and false theta functions.- H. Murakami and Anh T. Tran, On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real number.- J. Murakami and A. T. Tran, Potential function, A-polynomial and Reidemeister torsion of hyperbolic links.- H. Nakamura and D. Shiraishi, Landen?s trilogarithm functional equation and ?-adic Galois multiple polylogarithms.- T. Ohtsuki, On the Bloch groups of finite fields and their quotients by the relation corresponding to a tetrahedral symmetry.- R. Tange, On adjoint homological Selmer modules for SL2-augmented tautological representations of knot groups.- J. Ueki and A. Yasuda, A note on units and surfaces.- M. Wakui, -----deformed integers derived from pairs of coprime integers and its applications.- Z. Wojtkowiak, Canonical One-cocycle and Main Conjecture, I.- Hyuga Yoshizaki, Weber?s class number problem and its variants.
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