Topics in Knot Theory

ISBN-13: 9789401047425 / Angielski / Miękka / 2012 / 353 str.

M. E. Bozhuyuk

Opis

Topics in Knot Theory is a state of the art volume which presents surveys of the field by the most famous knot theorists in the world. It also includes the most recent research work by graduate and postgraduate students. The new ideas presented cover racks, imitations, welded braids, wild braids, surgery, computer calculations and plottings, presentations of knot groups and representations of knot and link groups in permutation groups, the complex plane and/or groups of motions.
For mathematicians, graduate students and scientists interested in knot theory.

Spis treści

Knot Projections and Knot Coverings; M.E. Bozhüyük. Knots and Knot Spaces; G. Burde. Knot Groups; G. Burde. An Introduction to Species and the Rack Space; R. Fenn. Introduction to Topological Imitations of (3,1)-Dimensional Manifold Pairs; A. Kawauchi. A Wild Variation of Artin's Braids; S. Moran. Invariants of Links and 3-Manifolds from Skein Theory and from Quantum Groups; H.R. Morton. Classical Invariants in Knot Theory; K. Murasugi. The Quest for a Knot with Trivial Jones Polynomial: Diagram Surgery and the Temperley--Lieb Algebra; D. Rolfsen. Twisted Topological Invariants associated with Representations; Shicheng Wang, Boju Jiang. On the Alexander and Jones Polynomial; H. Zieschang. Hyperbolic 3-Dimensional Orbifolds; M.A. Hagelberg. Irregular Dihedral Branched Coverings of Knots; T. Harikae, Y. Uchida. 2-Dimensional Braids and Chart Descriptions; S. Kamada. On Links embedded into Surfaces of Heegaard Splittings of S3; O. Karalashvili. A Search for Kernels of Burau Representations; D.M. Kim. The Witten--Reshitikhin--Turaev Invariant for Three Manifolds; R. Rimanyi. Index.