For any $g\ge 3$, we construct genus-$g$ Lefschetz fibrations over the two-sphere whose slopes are arbitrarily close to $2$. The total spaces of the Lefschetz fibrations can be chosen to be minimal and simply connected. It is also shown that the infimum and the supremum of slopes of all Lefschetz fibrations over the two-sphere are not realized as slopes.

中文翻译：

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低斜率 Lefschetz 纤维

对于任何$G\ge \mathrm{3个}$，我们构建类-$G$斜率任意接近的双球面上的 Lefschetz 纤维化$\mathrm{2个}$. Lefschetz 纤维的总空间可以选择为最小且简单连接。还表明，双球面上所有 Lefschetz 纤维的斜率的下界和上界并未实现为斜率。