Hyperbolic small knots in spherical manifolds

TL;DR

This paper constructs explicit examples of hyperbolic small knots within most closed orientable spherical 3-manifolds, addressing a conjecture about the existence of small knots in certain 3-manifolds.

Contribution

It provides the first explicit examples of hyperbolic small knots in a broad class of spherical 3-manifolds, expanding understanding of knot embeddings in 3-manifold topology.

Findings

Explicit hyperbolic small knots found in most closed orientable spherical 3-manifolds

Addresses Lopez's conjecture on small knots in non-Haken 3-manifolds

Expands the catalog of known small knots in spherical manifolds

Abstract

It was conjectured by Lopez that every closed irreducible non-Haken 3-manifold contains a small knot. In this paper, we give explicit examples of hyperbolic small knots in most closed orientable spherical 3-manifolds other than prism manifolds.