With hundreds of worked examples, exercises and illustrations, this detailed exposition of
the theory of Vassiliev knot invariants opens the field to students with little or no knowledge …

We study random knots and links in R^ 3 R 3 using the Petaluma model, which is based on
the petal projections developed in 2. In this model we obtain a formula for the limiting …

On the First Two Vassiliev Invariants Page 1 On the First Two Vassiliev Invariants Simon
Willerton CONTENTS 1. Introduction 2. On V2 and V3 3. Plots for Knots With up to 14 Crossings …

The topology of moduli spaces of classical knots and of long knots was much studied in
Refs.[5–8, 25]. In particular, there is a complete description of the homotopy type and of the …

In this paper finite type invariants (also known as Vassiliev invariants) of pure braids are
considered from a group-theoretic point of view. New results include a construction of a …

The based loop space of a configuration space of points in a Euclidean space can be
viewed as a space of pure braids in a Euclidean space of one dimension higher. We …

Although it is known that the dimension of the Vassiliev invariants of degree three of long
virtual knots is seven, the complete list of seven distinct Gauss diagram formulas has been …

This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with
a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers …

We use rational formality of configuration spaces and the bar construction to study the
cohomology of the space of braids in dimension four or greater. We provide a diagram …

Generalizing a result of Domergue and Donato, it is shown that if the transition from degree
n weight system to type n Vassiliev knot invariant is thought of as n steps of integration, then …