Knot Theory

Second Edition

Vassily Olegovich Manturov (Moscow State University, Russia)

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English

CRC Press
30 September 2020

Mathematics & Sciences; Geometry; Mathematical physics

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 alge-bra. 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 this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text.

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.

By: Vassily Olegovich Manturov (Moscow State University Russia)
Imprint: CRC Press
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 1.070kg
ISBN: 9780367657291
ISBN 10: 0367657295
Pages: 560
Publication Date: 30 September 2020
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Vassily Olegovich Manturov is professor of Geometry and Topology at Bauman Moscow State Technical University.

Reviews for Knot Theory: Second Edition

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