Meridional Rank of Knots Whose Exterior is a Graph Manifold

TL;DR

This paper proves that for a broad class of knots, specifically those with a graph manifold exterior, the meridional rank equals the bridge number, advancing understanding of knot invariants.

Contribution

It establishes that for knots with a graph manifold exterior, the meridional rank and bridge number are equal, partially answering a longstanding question.

Findings

Meridional rank equals bridge number for knots with graph manifold exterior

Includes all knots whose exterior is a graph manifold

Provides partial resolution to a question by Cappell and Shaneson

Abstract

We prove for a large class of knots that the meridional rank coincides with the bridge number. This class contains all knots whose exterior is a graph manifold. This gives a partial answer to a question of S. Cappell and J. Shaneson, see problem 1.11 on Kirby's list.