Mathematical Sciences: Topology

本项目涉及广泛的拓扑主题，从Swan研究的代数k理论到Orr研究的结理论。中心焦点是同伦理论和高维流形理论。Hopkins和Devinatz研究稳定同伦理论的全局结构。Stover研究了不稳定同伦理论的结构。May和Liulevicius研究了等变代数拓扑中的各种主题。Rothenberg和Weinberger研究流形和几何拓扑相关领域的群体作用。来自丹麦的马德森将继续与罗森伯格就有限群体行动进行合作。另有四名高级研究生在教师指导下从事相关研究。

This project deals with a broad range of topics in and around topology, from algebraic K-theory, studied by Swan, to knot theory, studied by Orr. The central foci are homotopy theory and high-dimensional manifold theory. Hopkins and Devinatz study the global structure of stable homotopy theory. Stover studies the structure of unstable homotopy theory. May and Liulevicius study a variety of topics in equivariant algebraic topology. Rothenberg and Weinberger study group actions on manifolds and related areas of geometric topology. Madsen, visiting from Denmark, will continue joint work with Rothenberg on finite group actions. Four advanced graduate students are also engaged in related research under faculty direction.