Mathematical Sciences: Topology, Geometry and Analysis of Group Actions and Foliations

本研究项目中解决的问题在 微分拓扑学领域。 他们的共同主题是发展 群作用的几何和拓扑之间的关系， 叶理，它们的上同调不变量，以及解析 微分算子的不变量 他们的几何。 史蒂文·赫德将致力于阿诺索夫的刚性 “大”群的作用;关于开群的“无穷大拓扑” 流形，基于微分的K-理论不变量 算子;关于低维Anosov分类 利用次类和模空间， 拟对称映射和椭圆算子的谱 在叶理的叶子上，使用测地线流的动力学 的叶理。 这一系列问题涉及自然物体， 流形，即局部欧几里得几何空间。 的 所处理的性质是这样的事情， 对象和在其上定义的流，所有这些都将由 代数和分析的各种技术。

The problems addressed in this research project are in the area of differential topology. Their common theme is to develop relations between the geometry and topology of group actions and foliations, their cohomology invariants, and the analytic invariants of differential operators naturally associated with their geometry. Steven Hurder will work on rigidity of Anosov actions of "large" groups; on the "topology-at-infinity" of open manifolds, based on K-theory invariants of differential operators; on the classifications of low-dimensional Anosov diffeomorphisms, using secondary classes and moduli spaces for quasi-symmetric maps; and on the spectrum of elliptic operators on leaves of foliations, using the dynamics of the geodesic flow of the foliation. This collection of problems concerns natural objects, manifolds, i.e. locally Euclidean geometric spaces. The properties dealt with are such things as symmetry of these objects and flows defined on them, all to be investigated by a variety of techniques from algebra and analysis.