Mathematical Sciences: Algebraic Surfaces and 4-Manifold Topology

将研究单连通代数曲面和其他光滑4-流形的拓扑。本课程将讨论如下问题：代数曲面在连通和下的表现如何？哪些4-流形是代数曲面的和？唐纳森不变量如何定义为拓扑学？代数曲面是由多项式方程定义的，这是人们可以使用的最基本的方程。关于这种曲面的非常自然和容易表达的问题仍然没有得到回答，这是对拓扑学领域的一种挑战和几乎是一种指责。

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.