# Computing Genera of Satellite Tunnel Number One Knots and Torti-rational Knots

## TL;DR

This paper presents an algorithmic approach to compute the genus and slopes of minimal genus Seifert surfaces for satellite tunnel number one knots and torti-rational knots, utilizing Floyd and Hatcher's tools.

## Contribution

It introduces an implementation of an algorithm to determine genus and slopes for these knots, advancing computational knot theory.

## Key findings

- Algorithm successfully computes genus and slopes for the specified knots.
- Provides a practical tool based on Floyd and Hatcher's methods.
- Enhances understanding of the structure of satellite tunnel number one and torti-rational knots.

## Abstract

The genus of satellite tunnel number one knots and torti-rational knots is computed using the tools introduced by Floyd and Hatcher. An implementation of an algorithm is given to compute genus and slopes of minimal genus Seifert surfaces for such knots.