## An Upper Bound on Reidemeister Moves

Alexander Coward

Sydney University

Abstract

Given any two diagrams of the same knot or link, we provide an explicit upper bound on the number of Reidemeister moves required to pass between them in terms of the number of crossings in each diagram. This provides a new and conceptually simple solution to the equivalence problem for knot and links. This is joint work with Marc Lackenby.