Bibliographic Information

Knot theory

by Vassily Manturov

CRC Press, c2018

2nd ed

  • : hardback

Available at  / 8 libraries

Search this Book/Journal

Note

"A Chapman & Hall book"--Cover

Includes bibliographical references (p. 529-553) and index

Description and Table of Contents

Description

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

  • 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.

by "Nielsen BookData"

Details

  • NCID
    BB25955820
  • ISBN
    • 9781138561243
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Boca Raton
  • Pages/Volumes
    xix, 559 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
Page Top