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

Abstract

The space of Gauss diagram formulas that are knot invariants is introduced by Goussarov–Polyak–Viro in 2000; it is extended to nanophrases by Gibson–Ito in 2011. However, known invariants in concrete presentations of Gauss diagram formulas are very limited, even in the one-component case. This paper gives a recipe to obtain explicit forms of Gauss diagram formulas that are invariants of virtual links with base points or tangles. As an application, we introduce a new construction of Gauss diagram formulas of [Formula: see text]-bouquets and how to give link invariants that do not change with base point moves, including a reconstruction of the Milnor’s triple linking number.