ABSTRACT

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.

part I|129 pages

Knots, links, and invariant polynomials

part II|92 pages

Theory of braids

part III|78 pages

Vassiliev’s invariants. Atoms and d-diagrams

part IV|142 pages

Virtual knots

chapter 18|32 pages

Invariant polynomials of virtual links

chapter 19|11 pages

Generalised Jones–Kauffman polynomial

chapter 20|10 pages

Long virtual knots and their invariants

chapter 21|16 pages

Virtual braids

chapter 22|50 pages

Khovanov homology of virtual knots

part V|54 pages

Knots, 3-manifolds, and Legendrian knots

chapter 23|21 pages

3-Manifolds and knots in 3-manifolds

chapter 24|16 pages

Heegaard–Floer homology

chapter 25|14 pages

Legendrian knots and their invariants