# On families of fibred knots with equal Seifert forms

## TL;DR

This paper constructs infinite families of fibred, strongly quasipositive knots with identical Seifert forms to certain torus knots, sharing many invariants but differing in geometric properties and ribbon concordance status.

## Contribution

It introduces a method to generate infinite families of fibred knots with identical Seifert forms and invariants, yet distinct geometric and concordance properties.

## Key findings

- Knots have maximal signatures and four-genus.
- Homological monodromies and Alexander modules are identical.
- Knots differ in geometric stretching factors and ribbon concordance.

## Abstract

For every genus $g\geq 2$, we construct an infinite family of strongly quasipositive fibred knots having the same Seifert form as the torus knot $T(2,2g+1)$. In particular, their signatures and four-genera are maximal and their homological monodromies (hence their Alexander module structures) agree. On the other hand, the geometric stretching factors are pairwise distinct and the knots are pairwise not ribbon concordant.