Milnor's triple linking number and Gauss diagram formulas of 3-bouquet graphs

Abstract

In this paper, we focus on two invariants which sum is the Milnor's triple linking number of 3-component links. The two invariants give strictly stronger link homotopy invariants than the Milnor's triple linking number. We also have found a series of integer-valued invariants derived from four terms which sum equals the Milnor's triple linking number that is torsion-valued. We apply this structure to give invariants of 3-bouquet graphs.