Communications in Analysis and Geometry

Volume 29 (2021)

Number 2

On families of fibred knots with equal Seifert forms

Pages: 465 – 482

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n2.a6

Author

Filip Misev (Institut de Mathématiques, Université Aix-Marseille, France)

Abstract

For every genus $g \geqslant 2$, we construct an infinite family of strongly quasipositive fibred knots $K_n$ having the same Seifert form as the torus knot $T(2, 2g + 1)$. In particular, their homological monodromies agree and their signatures and four-genera are maximal: $\lvert \sigma (K_n) \rvert = 2g_4 (K_n) = 2g$. On the other hand, the geometric stretching factors are pairwise distinct and the knots are pairwise not ribbon concordant.

The author is supported by the Swiss National Science Foundation (#168676).

Received 7 December 2017

Accepted 4 June 2018