Communications in Analysis and Geometry
Volume 29 (2021)
On families of fibred knots with equal Seifert forms
Pages: 465 – 482
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
Published 19 April 2021