Hyperbolic knots with a large toroidal surgery

TL;DR

This paper constructs an infinite family of hyperbolic knots that admit a special type of surgery resulting in a graph manifold with five disjoint incompressible tori, highlighting complex topological structures.

Contribution

It introduces a new infinite family of hyperbolic knots with exceptional surgeries producing complex graph manifolds with multiple incompressible tori.

Findings

Existence of an infinite family of hyperbolic knots with specified surgeries.

Construction of surgeries yielding graph manifolds with five disjoint incompressible tori.

Identification of properties of these knots and their surgeries.

Abstract

We show an infinite family of hyperbolic knots that have an exceptional surgery producing a graph manifold containing five disjoint, and non parallel incompressible tori.