Mathematical Sciences: Group Proposal in Topology

本项目涵盖了拓扑和代数、代数k理论和代数几何等相关领域的广泛课题研究。一个重点是稳定同伦理论中的全局代数结构，应用于协共、拓扑Hochschild同调和代数k理论等主题。另一个是代数和拓扑向量束的研究以及代数变种的Hochschild同调。另一个是流形的解析和组合扭转不变量的研究。芝加哥大学对代数和几何拓扑的研究多年来一直在探索拓扑内部的领域以及拓扑与代数几何和微分几何之间的边界领域。这里发展出来的思想，例如算子的概念，已经被应用于从数学物理到组合群论的各个领域。参与该项目的研究生和博士后离开芝加哥后，将获得特别广泛的跨学科培训和背景。＊＊＊

9423300 May This project encompasses research in a wide variety of topics in topology and related areas of algebra, algebraic K-theory and algebraic geometry. One focus is global algebraic structures in stable homotopy theory, with applications to such topics as cobordism, topological Hochschild homology, and algebraic K-theory. Another is the study of algebraic and topological vector bundles and of Hochschild homology for algebraic varieties. Another is the study of analytic and combinatorial torsion invariants of manifolds. Research in algebraic and geometric topology at the University of Chicago has for many years explored areas both internal to topology and areas on the borders between topology and algebraic geometry and differential geometry. Ideas developed here, for example the notion of an operad, have been used in diverse fields, from mathematical physics to combinatorial group theory. Graduate students and postdocs involved in the project leave Chicago with especially broad interdisciplinary training and background. ***