Mathematical Sciences: Topology

这个项目涵盖了广泛的主题，在代数和 几何拓扑学 更具体地说，研究人员计划 研究分支覆盖和有理函数; 某些性质的有限性和其他类似算术的性质 离散群;群的几何不变量; Steenrod's 问题在各种同变上下文中，包括RO（G）- 分次同调;同伦G-作用;等变光滑， 三角剖分理论;光滑等变Rn-丛;自由 产品和外科手术结;叠层在3流形; 受控简单同伦理论;参数空间 复映射的迭代。 这些研究是基础， 了解许多物理模型的定性行为 或生物学甚至社会系统。 人们常常想知道 关于稳定性，周期性和其他定性性质， 模型尽可能多或超过一个想要明确和详细 数值解 每当定性行为有争议时， 在某种程度上肯定涉及到拓扑学。

This project covers a wide range of topics in algebraic and geometric topology. More specifically, the researchers plan to study the following: branched coverings and rational functions; finiteness and other arithmetic-like properties of certain discrete groups; geometric invariants of groups; Steenrod's problem in various equivariant contexts, including that of RO(G)- graded homology; homotopy G-actions; equivariant smoothing and triangulation theory; smooth, equivariant Rn-bundles; free products and surgery on knots; laminations in 3-manifolds; controlled simple homotopy theory; parameter spaces for iterations of complex maps. Such studies are basic to understanding the qualitative behavior of many models of physical or biological or even social systems. One often wishes to know about stability, periodicity, and other qualitative properties of models as much or more than one wants explicit and detailed numerical solutions. Whenever qualitative behavior is at issue, topology is sure to be involved at some level.