Moebius bands with a quasipositive fibred hole

On families of fibred knots with equal Seifert forms

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.

无L-空间手术的紧纤维结

Tight fibred knots without L-space surgeries

本文证明对每个固定亏格$g\geq 2$，存在无穷多个纤维且强拟正的结，它们与同亏格环面结代数协边，但不承认L-空间手术。