Milnor–Orr Invariants from the Kontsevich Invariant

Abstract

As nilpotent studies in knot theory, we focus on invariants of Milnor, Orr and Kontsevich. We show that the Orr invariant of degree $k$ is equivalent to the tree reduction of the Kontsevich invariant of degree $<2k$. Furthermore, we will see a close relation between the Orr invariant and the Milnor invariant, and discuss a method of computing them.