On families of fibred knots with equal Seifert forms

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.

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

Received 7 December 2017

Accepted 4 June 2018

Published 19 April 2021