Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov
Publisher: arXiv 2014
Number of pages: 66
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 second section of the paper introduces the theory and discusses some problems in that context.
Home page url
Download or read it online for free here:
by Louis H. Kauffman - arXiv
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.
by Andrew Ranicki - Oxford University Press
Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.
by Nigel Hitchin
Geometry of Surfaces by Nigel Hitchin is a textbook on surfaces. However the author is also going to try and consider surfaces intrinsically, or abstractly, and not necessarily embedded in three-dimensional Euclidean space.
by Andrew Ranicki - Cambridge University Press
This is the first treatment of the applications of the lower K- and L-groups to the topology of manifolds such as Euclidean spaces, via Whitehead torsion and the Wall finiteness and surgery obstructions. Only elementary constructions are used.