The Schubert normal form of a 3-bridge link and the 3-bridge link group

Abstract

We introduce the Schubert form for a [Formula: see text]-bridge link diagram, as a generalization of the Schubert normal form of a [Formula: see text]-bridge link. It consists of a set of six positive integers, written as [Formula: see text], with some conditions and it is based on the concept of [Formula: see text]-butterfly. Using the Schubert normal form of a [Formula: see text]-bridge link diagram, we give two presentations of the 3-bridge link group. These presentations are given by concrete formulas that depend on the integers [Formula: see text]. The construction is a generalization of the form the link group presentation of the [Formula: see text]-bridge link [Formula: see text] depends on the integers [Formula: see text] and [Formula: see text].