Mathematical Sciences: Algebraic Surfaces and 4-Manifold Topology

单连通代数曲面的拓扑和 其他光滑4-流形将被研究。 问题，如 将解决以下问题：代数曲面的行为如何 在连接的总和？ 哪些四维流形是代数和 表面？ 如何定义唐纳森的不变量 拓扑学？ 代数曲面由多项式方程定义， 最基本的方程式 非常自然， 关于这种表面的简单的问题仍然存在 没有回答的问题是一个挑战，几乎是对这个领域的指责。 拓扑学

The topology of simply-connected algebraic surfaces and other smooth 4-manifolds will be studied. Questions such as the following will be addressed: How do algebraic surfaces behave under connected sum? Which 4-manifolds are sums of algebraic surfaces? How can Donaldson's invariants be defined topologically? Algebraic surfaces are defined by polynomial equations, the most elemetary equations one could use. That very natural and easily formulated questions about such surfaces still remain unanswered stands as a challenge and almost a rebuke to the field of topology.