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Author : Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 119 pages
File Size : 40,7 Mb
Release : 1965-03-21
Category : Mathematics
ISBN : 9780691079912
The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.
Author : Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 119 pages
File Size : 47,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882038
The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.
Author : Jerome Minkus
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 46,6 Mb
Release : 1982
Category : Knot theory
ISBN : 9780821822555
In this paper a family of closed oriented 3 dimensional manifolds {[italic]M[subscript italic]n([italic]k,[italic]h)} is constructed by pasting together pairs of regions on the boundary of a 3 ball. The manifold [italic]M[subscript italic]n([italic]k,[italic]h) is a generalization of the lens space [italic]L([italic]n,1) and is closely related to the 2 bridge knot or link of type ([italic]k,[italic]h). While the work is basically geometrical, examination of [lowercase Greek]Pi1([italic]M[subscript italic]n([italic]k,[italic]h)) leads naturally to the study of "cyclic" presentations of groups. Abelianizing these presentations gives rise to a formula for the Alexander polynomials of 2 bridge knots and to a description of [italic]H1([italic]M[subscript italic]n([italic]k,[italic]h), [italic]Z) by means of circulant matrices whose entries are the coefficients of these polynomials.
Author : Ken’ichi Ohshika,Athanase Papadopoulos
Publisher : Springer Nature
Page : 724 pages
File Size : 45,7 Mb
Release : 2020-12-07
Category : Mathematics
ISBN : 9783030559281
This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.
Author : Hitoshi Murakami,Yoshiyuki Yokota
Publisher : Springer
Page : 120 pages
File Size : 45,7 Mb
Release : 2018-08-15
Category : Science
ISBN : 9789811311505
The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called R-matrix that is associated with the N-dimensional representation of the Lie algebra sl(2;C). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume. In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the case of hyperbolic knots by showing how the summation formula for the colored Jones polynomial “looks like” the hyperbolicity equations of the knot complement. We also describe a generalization of the volume conjecture that corresponds to a deformation of the complete hyperbolic structure of a knot complement. This generalization would relate the colored Jones polynomial of a knot to the volume and the Chern–Simons invariant of a certain representation of the fundamental group of the knot complement to the Lie group SL(2;C). We finish by mentioning further generalizations of the volume conjecture.
Author : C N Yang,M L Ge
Publisher : World Scientific
Page : 480 pages
File Size : 55,7 Mb
Release : 1994-02-24
Category : Science
ISBN : 9789814502788
The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors. Contents:On the Combinatorics of Vassiliev Invariants (J S Birman)Solvable Methods, Link Invariants and Their Applications to Physics (T Deguchi & M Wadati)Quantum Symmetry in Conformal Field Theory by Hamiltonian Methods (L D Faddeev)Yang-Baxterization & Algebraic Structures (M L Ge, K Xue, Y S Wu)Spin Networks, Topology and Discrete Physics (L H Kauffman)Tunnel Numbers of Knots and Jones-Witten Invariants (T Kohno)Knot Invariants and Statistical Mechanics: A Physicist's Perspective (F Y Wu)and other papers Readership: Mathematical physicists. keywords:Braid Group;Knot Theory;Statistical Mechanics “It has been four years since the publication in 1989 of the previous volume bearing the same title as the present one. Enormous amounts of work have been done in the meantime. We hope the present volume will provide a summary of some of these works which are still progressing in several directions.” from the foreword by C N Yang
Author : William Menasco,Morwen Thistlethwaite
Publisher : Elsevier
Page : 502 pages
File Size : 46,8 Mb
Release : 2005-08-02
Category : Mathematics
ISBN : 0080459544
This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics
Author : Robion C. Kirby,Laurence C. Siebenmann
Publisher : Princeton University Press
Page : 368 pages
File Size : 55,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881505
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Author : Lee Paul Neuwirth
Publisher : Unknown
Page : 128 pages
File Size : 42,9 Mb
Release : 1940
Category : Knot theory
ISBN : UCBK:C058341904
Author : Richard S. Palais
Publisher : Princeton University Press
Page : 376 pages
File Size : 48,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882045
The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.
Author : Chen Chung Chang,H. Jerome Keisler
Publisher : Princeton University Press
Page : 165 pages
File Size : 44,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882052
This is a study of the theory of models with truth values in a compact Hausdorff topological space.
Author : Yukio Matsumoto,José María Montesinos-Amilibia
Publisher : Springer
Page : 240 pages
File Size : 51,6 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9783642225345
The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Author : John Frank Adams
Publisher : Princeton University Press
Page : 230 pages
File Size : 48,8 Mb
Release : 1978-09-01
Category : Mathematics
ISBN : 9781400821259
The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.
Author : C N Yang,M L Ge
Publisher : World Scientific
Page : 336 pages
File Size : 51,5 Mb
Release : 1991-06-05
Category : Electronic
ISBN : 9789814507424
Contents:Notes on Subfactors and Statistical Mechanics (V F R Jones)Polynomial Invariants in Knot Theory (L H Kauffman)Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev)Quantum Groups (L Faddeev et al.)Introduction to the Yang-Baxter Equation (M Jimbo)Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno)The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.)Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.)Quantum Field Theory and the Jones Polynomial (E Witten) Readership: Mathematical physicists.
Author : Ken’ichi Ohshika,Athanase Papadopoulos
Publisher : Springer Nature
Page : 525 pages
File Size : 55,6 Mb
Release : 2022-08-02
Category : Mathematics
ISBN : 9783030975609
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.