Mathematical Sciences: Geometry and Topology of Complex Variables and Manifolds in Low Dimensions

沃尔特·诺伊曼将继续研究复杂曲线和曲面的拓扑及其奇点，特别是复杂结构的存在对相关的三维和四维流形的拓扑和拓扑不变量的影响。他还将研究低维实流形和复流形上的几何结构，包括奇异结构、结构的变形、它们的不变量，以及与不变量相关的算术问题。几何和代数之间的显著联系随处可见。几何和物理的基础是3维和4维流形。它们的拓扑性质是连通性和结性等基本性质。令人印象深刻的是，代数技术在研究这些性质方面是多么有效。

Walter Neumann will continue his study of the topology of complex curves and surfaces and their singularities, particularly the influence of the existence of complex structures on the topology and topological invariants of the associated 3- and 4-manifolds. He will also study geometric structures on real and complex manifolds in low dimensions, including singular structures, deformation of structures, their invariants, and arithmetic questions related to the invariants. Remarkable connections between geometry and algebra are uncovered at every turn. Basic to geometry and physics are 3- and 4-dimensional manifolds. Their topological properties are such fundamental things as connectedness and knottedness. It is impressive how effective algebraic techniques have been in investigating these properties.