Boundary-reducing surgeries and bridge number

TL;DR

This paper constructs hyperbolic knots within 3D handlebodies that have large bridge numbers and admits Dehn surgeries resulting in boundary-reducible manifolds, expanding understanding of knot complexity and surgery outcomes.

Contribution

It provides explicit examples of hyperbolic knots with large bridge numbers in handlebodies that undergo boundary-reducing Dehn surgeries, a novel contribution to knot theory and 3-manifold topology.

Findings

Existence of hyperbolic knots with arbitrarily large bridge number in handlebodies.

Such knots admit Dehn surgeries yielding boundary-reducible manifolds.

New examples illustrating the relationship between bridge number and surgery outcomes.

Abstract

Let $M$ be a $3$--dimensional handlebody of genus $g$. This paper gives examples of hyperbolic knots in $M$ with arbitrarily large genus $g$ bridge number which admit Dehn surgeries which are boundary-reducible manifolds.