论文标题
表面上的奇异振动
Singular fibrations over surfaces
论文作者
论文摘要
奇异振动概括了4个manifolds在表面上的Achiral Lefschetz纤维，同时共享了它们的某些特性。例如，相对最小的奇异振动取决于它们的单片。我们解释了如何用单个奇异性构建奇异振动的示例，而松本构建了球体的奇异振动$ s^4 $。 Hirzebruch和Hopf的先前结果在有限的许多奇点上与Neumann和Rudolph在HOPF不变的工作有关。最终，我们证明，封闭的可定向的4个manifolds具有较大的betti数字，而第二次贝蒂（Betti）数字消失了，不承认奇异振动。
Singular fibrations generalize achiral Lefschetz fibrations of 4-manifolds over surfaces while sharing some of their properties. For instance, relatively minimal singular fibrations are determined by their monodromy. We explain how to construct examples of singular fibrations with a single singularity and Matsumoto's construction of singular fibrations of the sphere $S^4$. Previous results of Hirzebruch and Hopf on 2-plane fields with finitely many singularities are outlined in connection with the work of Neumann and Rudolph on the Hopf invariant. Eventually, we prove that closed orientable 4-manifolds with large first Betti number and vanishing second Betti number do not admit singular fibrations.
