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

TL;DR

This paper introduces new functions and invariants related to Milnor's triple linking number, providing formulas for 3-bouquet graphs and expanding understanding of link homotopy invariants.

Contribution

It presents novel functions and invariants that relate to Milnor's triple linking number and applies these to 3-bouquet graphs, advancing link homotopy theory.

Findings

Defined functions whose difference equals Milnor's triple linking number

Constructed new integer-valued link homotopy invariants

Derived invariants from four-term sums related to Milnor's number

Abstract

In this paper, we introduce two functions such that the subtraction corresponds to the Milnor's triple linking number; the addition obtains a new integer-valued link homotopy invariant of $3$-component links. We also have found a series of integer-valued invariants derived from four terms whose sum equals the Milnor's triple linking number. We apply this structure to give invariants of $3$-bouquet graphs.