On hyperbolic L-space knots with braid index four and tunnel number two

TL;DR

This paper introduces the first infinite family of strongly invertible hyperbolic L-space knots with braid index four and tunnel number two, expanding known examples in this category.

Contribution

It provides a new infinite family of such knots, including previously known examples, enriching the classification of hyperbolic L-space knots.

Findings

Identifies an infinite family of knots with specified properties

Includes known examples t10496 and o9_34409 within this family

Expands the understanding of hyperbolic L-space knots with these invariants

Abstract

There are only three known strongly invertible hyperbolic L-space knots with braid index four and tunnel number two. They are t09284, t10496 and o9_34409 in the SnapPy census. In this paper, we give the first infinite family of strongly invertible hyperbolic L-space knots with braid index four and tunnel number two that includes t10496 and o9_34409.