Some 4-manifold geometry from hyperbolic knots in S^3

TL;DR

This paper explores the construction of a 4-manifold with unusual metric properties, utilizing hyperbolic knots in S^3, and investigates whether these properties indicate a single or multiple manifolds.

Contribution

It introduces a novel construction linking hyperbolic knot complements in S^3 to 4-manifolds with unique metric features.

Findings

Identification of a 4-manifold with curious metric properties

Connection between hyperbolic knots and 4-manifold geometry

Potential multiple manifolds masquerading as one

Abstract

A 4-manifold is constructed with some curious metric properties; or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious. Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on their complements play a role in this story.