2 problems

Let $M$ be a smooth $4$-manifold and let $f_1,f_2:M\rightarrow S^2$ be homotopic simplified broken Lefschetz fibrations. A flip-and-slip modification is a modification of a simplif…

Let $\mathbb{CP}^2$ denote the complex projective plane, and call a broken Lefschetz fibration achiral if it allows Lefschetz critical points with nonstandard orientations. Gay–Kir…