# Knot Theory

DOI link for Knot Theory

Knot Theory book

# Knot Theory

DOI link for Knot Theory

Knot Theory book

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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.

## TABLE OF CONTENTS

part I|129 pages

Knots, links, and invariant polynomials

chapter 8|23 pages

#### Lee-Rasmussen invariant, slice knots, and the genus conjecture

part II|92 pages

Theory of braids

part III|78 pages

Vassiliev’s invariants. Atoms and d-diagrams

chapter 15|20 pages

#### The Kontsevich integral and formulae for the Vassiliev invariants

part IV|142 pages

Virtual knots

part V|54 pages

Knots, 3-manifolds, and Legendrian knots