# Prime knot complements with meridional essential surfaces of arbitrarily high genus

## TL;DR

This paper proves that there are infinitely many prime knots whose complements contain meridional essential surfaces with two boundary components and arbitrarily high genus, expanding understanding of knot complement topology.

## Contribution

It demonstrates the existence of infinitely many prime knots with high genus meridional essential surfaces in their complements, a new result in knot theory.

## Key findings

- Existence of infinitely many prime knots with specified properties.
- Construction of meridional essential surfaces with arbitrarily high genus.
- Advancement in understanding the topology of knot complements.

## Abstract

We show the existence of infinitely many prime knots each of which having in their complements meridional essential surfaces with two boundary components and arbitrarily high genus.