A representation of Milnor's triple linking number by chord diagrams and doodle invariants

Abstract: From the work of X. S. Lin and Z. Wang, it follows that degree two knot invariant admits a decomposition into the sum of a Gauss diagram count and a term involving Arnold invariants. In this paper we establish an analogous description for Milnor's triple linking number - likewise of degree two - showing that it can be represented in terms of counts of certain chord diagrams together with doodle invariants.