Knot Theory : Second Edition /

"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),...

Full description

Bibliographic Details
Main Author:	Manturov, Vassily (Author)
Corporate Author:	Taylor & Francis
Other Authors:	Nikonov, Igor Mikhailovich (Editor)
Format:	eBook
Language:	English
Published:	Boca Raton, FL : CRC Press, 2018.
Edition:	Second edition.
Subjects:	General Physics Geometry Mathematical Physics MATHnetBASE SCI-TECHnetBASE STMnetBASE Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

part, I Knots, links, and invariant polynomials
chapter 1 Introduction / Vassily Manturov
chapter 2 Reidemeister moves. Knot arithmetics / Vassily Manturov
chapter 3 Links in 2-surfaces in ℝ3. Simplest link invariants / Vassily Manturov
chapter 4 Fundamental group. The knot group / Vassily Manturov
chapter 5 The knot quandle and the Conway algebra / Vassily Manturov
chapter 6 Kauffman's approach to Jones polynomial / Vassily Manturov
chapter 7 Properties of Jones polynomials. Khovanov's complex / Vassily Manturov
chapter 8 Lee-Rasmussen invariant, slice knots, and the genus conjecture / Vassily Manturov
part, II Theory of braids
chapter 9 Braids, links and representations of braid groups / Vassily Manturov
chapter 10 Braids and links. Braid construction algorithms / Vassily Manturov
chapter 11 Algorithms of braid recognition / Vassily Manturov
chapter 12 Markov's theorem. The Yang-Baxter equation / Vassily Manturov
part, III Vassiliev's invariants. Atoms and d-diagrams
chapter 13 Definitions and basic notions of Vassiliev invariant theory / Vassily Manturov
chapter 14 The chord diagram algebra / Vassily Manturov
chapter 15 The Kontsevich integral and formulae for the Vassiliev invariants / Vassily Manturov
chapter 16 Atoms, height atoms and knots / Vassily Manturov
part, IV Virtual knots
chapter 17 Virtual knots. Basic definitions and motivation / Vassily Manturov
chapter 18 Invariant polynomials of virtual links / Vassily Manturov
chapter 19 Generalised Jones-Kauffman polynomial / Vassily Manturov
chapter 20 Long virtual knots and their invariants / Vassily Manturov
chapter 21 Virtual braids / Vassily Manturov
chapter 22 Khovanov homology of virtual knots / Vassily Manturov
part, V Knots, 3-manifolds, and Legendrian knots
chapter 23 3-Manifolds and knots in 3-manifolds / Vassily Manturov
chapter 24 Heegaard-Floer homology / Vassily Manturov
chapter 25 Legendrian knots and their invariants / Vassily Manturov.