by Louis H. Kauffman
Publisher: arXiv 2004
Number of pages: 107
This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.
Home page url
Download or read it online for free here:
by Eiji Ogasa - arXiv
This is an introductory article on high dimensional knots for the beginners. Is there a nontrivial high dimensional knot? We first answer this question. We explain local moves on high dimensional knots and the projections of high dimensional knots.
by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov - arXiv
The purpose of this paper is to give an introduction to virtual knot theory and to record a collection of research problems that the authors have found fascinating. The paper introduces the theory and discusses some problems in that context.
by S.Chmutov, S.Duzhin, J.Mostovoy - Ohio State Universit
An introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. Written for readers with no background in this area, and we care more about the basic notions than about more advanced material.
by C.T.C. Wall, A. A. Ranicki - American Mathematical Society
This book represents an attempt to collect and systematize the methods and main applications of the method of surgery, insofar as compact (but not necessarily connected, simply connected or closed) manifolds are involved.