Finite-type knot invariants

By Robin Koytcheff

May 1, 2012

Abstract

Finite-type knot invariants (a.k.a Vassiliev invariants) are an important class of invariants in that they conjecturally separate knots. We will define them in elementary, purely combinatorial terms, drawing plenty of pictures. We'll prove some simple facts about them and compute at least one example. If time permits, we will discuss one way of constructing them via the configuration space integrals of Bott and Taubes.