# Tight fibred knots without L-space surgeries

## TL;DR

This paper constructs infinitely many fibred, strongly quasipositive knots of any fixed genus that do not admit L-space surgeries, despite resembling algebraic and L-space knots.

## Contribution

It demonstrates the existence of infinitely many knots with fixed genus that are fibred, strongly quasipositive, algebraically concordant to torus knots, yet do not admit L-space surgeries.

## Key findings

- Existence of infinitely many such knots for each genus g ≥ 2.
- These knots are algebraically concordant to torus knots T(2,2g+1).
- They do not admit surgeries to L-spaces.

## Abstract

We show there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery to an L-space, despite resembling algebraic knots and L-space knots in general: they are algebraically concordant to the torus knot $T(2,2g+1)$ of the same genus and they are fibred and strongly quasipositive.