CDBooK: Introduction to Vassiliev Knot invariants
by S.Chmutov, S.Duzhin, J.Mostovoy
Publisher: Ohio State Universit 2009
Number of pages: 460
This text provides an introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended for readers with no or little background in this area, and we care more about a clear explanation of the basic notions and constructions than about widening the exposition to more recent and more advanced material.
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by William P Thurston - Mathematical Sciences Research Institute
The text describes the connection between geometry and lowdimensional topology, it is useful to graduate students and mathematicians working in related fields, particularly 3-manifolds and Kleinian groups. Much of the material or technique is new.
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 - Springer
This book is an introduction to high-dimensional knot theory. It uses surgery theory to provide a systematic exposition, and it serves as an introduction to algebraic surgery theory, using high-dimensional knots as the geometric motivation.
by Louis H. Kauffman - University of Illinois at Chicago
This book is an introduction to knot theory and to Witten's approach to knot theory via his functional integral. Contents: Topics in combinatorial knot theory; State Models and State Summations; Vassiliev Invariants and Witten's Functional Integral.