Knot Theory: Second Edition
Autor Vassily Olegovich Manturoven Limba Engleză Hardback – 29 mar 2018
Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
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Specificații
ISBN-13: 9781138561243
ISBN-10: 113856124X
Pagini: 580
Ilustrații: 2 Tables, black and white; 289 Illustrations, black and white
Dimensiuni: 156 x 234 x 37 mm
Greutate: 2.2 kg
Ediția:2 New edition
Editura: CRC Press
Colecția CRC Press
ISBN-10: 113856124X
Pagini: 580
Ilustrații: 2 Tables, black and white; 289 Illustrations, black and white
Dimensiuni: 156 x 234 x 37 mm
Greutate: 2.2 kg
Ediția:2 New edition
Editura: CRC Press
Colecția CRC Press
Public țintă
ProfessionalCuprins
Knots, links, and invariant polynomials. Introduction. Reidemeister moves. Knot arithmetics. Links in 2-surfaces in R3.Fundamental group; the knot group. The knot quandle and the Conway algebra. Kauffman's approach to Jones polynomial. Properties of Jones polynomials. Khovanov's complex. Theory of braids. Braids, links and representations of braid groups. Braids and links. Braid construction algorithms. Algorithms of braid recognition. Markov's theorem; the Yang-Baxter equation. Vassiliev's invariants. Definition and Basic notions of Vassiliev invariant theory. The chord diagram algebra. The Kontsevich integral and formulae for the Vassiliev invariants. Atoms and d-diagrams. Atoms, height atoms and knots. The bracket semigroup of knots. Virtual knots. Basic definitions and motivation. Invariant polynomials of virtual links. Generalised Jones-Kauffman polynomial. Long virtual knots and their invariants. Virtual braids. Other theories. 3-manifolds and knots in 3-manifolds. Legendrian knots and their invariants. Independence of Reidemeister moves.
Notă biografică
Vassily Olegovich Manturov is professor of Geometry and Topology at Bauman Moscow State Technical University.
Recenzii
Praise for the first edition
This book is highly recommended for all students and researchers in knot theory, and to those in the sciences and mathematics who would like to get a flavor of this very active field.”
-Professor Louis H. Kauffman, Department of Mathematics, Statistics and Com-puter Science, University of Illinois at Chicago
This book is highly recommended for all students and researchers in knot theory, and to those in the sciences and mathematics who would like to get a flavor of this very active field.”
-Professor Louis H. Kauffman, Department of Mathematics, Statistics and Com-puter Science, University of Illinois at Chicago
Descriere
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and algebra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to the Second Edition; discusses Heegaard-Floer homology theory and A-polynomial of classical links. Updates throughout the book.