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Knot theory /

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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 algebra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A...

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Bibliographic Details
Main Author: Manturov, V. O. (Vasiliĭ Olegovich) (Author)
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: Boca Raton, FL : CRC Press, [2018]
Edition:Second edition.
Subjects:
Knot theory.
Théorie des nœuds.
MATHEMATICS > Topology.
Knot theory
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction
  • Reidemeister moves. Knot arithmetics
  • Links in 2-surfaces in R3. Simplest link invariants
  • 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
  • Lee-Rasmussen invariant, slice knots, and the genus conjecture
  • Braids, links and representations of braid groups
  • Braids and links. Braid construction algorithms
  • Algorithms of braid recognition
  • Markov's theorem. The Yang Baxter equation
  • Definitions and basic notions of Vassiliev invariant theory
  • The chord diagram algebra
  • The Kontsevich integral and formulae for the Vassiliev invariants
  • Atoms, height atoms and knots
  • Virtual knots. Basic definitions and motivation
  • Invariant polynomials of virtual links
  • Generalised Jones-Kauffman polynomial
  • Long virtual knots and their invariants
  • Virtual braids
  • Khovanov homology of virtual knots
  • 3-manifolds and knots in 3-manifolds
  • Heegaard-Floer homology
  • Legendrian knots and their invariants.