Mathematical Sciences: Manifolds and Algebraic Topology

数学科学：流形和代数拓扑

• 批准号: 9108269
• 负责人: William Browder
• 金额: $ 98.82万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9108269&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Manifolds; Algebraic; Topology

This project involves four senior research topologists (William Browder, Wu-chung Hsiang, John N. Mather, and William P. Thurston), one postdoctoral associate (Lang-Fang Wu), and three advanced graduate students. Their research topics are quite various. Browder will study free actions of certain topological groups on finite-dimensional spaces. He will also study fixed point theorems and regularity of minimal surfaces. Hsiang will work on a number of problems related to the cyclotomic trace map, including the notorious Novikov conjecture in L-theory as well as some more tractable ones. Mather's research deals with area-preserving diffeomorphisms of infinite cylinders. There are several hard conjectures about invariant curves under diffeomorphisms and their rotation numbers. Thurston will work toward his famous geometrization conjecture for 3-manifolds. In addition, he will work on automatic groups, self-similar tilings, one-dimensional real and complex dynamical systems, and other topics. Wu's research concerns the Ricci Flow equations on manifolds and orbifolds. All these topics are in the mainstream of research in topology. It is appropriate to involve graduate students in their study. For example, the geometrization conjecture of Thurston is a notoriously difficult problem. It subsumes the Poincare Conjecture, which dates to the turn of the century. Nevertheless, pieces of it have been the stuff of numerous Ph.D theses by Thurston's students for more than a decade.

该项目涉及四名高级研究拓扑学家 （William Browder，Wu-chung Hsiang，John N. Mather，and William P. Thurston），一名博士后助理（Lang-Fang Wu）和三名 高级研究生。 他们的研究课题相当 各种. Browder将研究某些拓扑的自由作用 有限维空间上的群 他还将研究固定 点定理和极小曲面的正则性。 项怀诚将致力于解决与 分圆迹映射，包括臭名昭著的诺维科夫猜想 以及一些更容易处理的理论。 Mather的研究涉及面积保持的非同态 无限的圆柱体。 有几个艰难的挑战， 仿射不变曲线及其旋转 号码 瑟斯顿将致力于他著名的几何化 关于三维流形的猜想 此外，他还将致力于 自动组、自相似切片、一维真实的和 复杂动力学系统及其他主题。 吴的研究涉及流形上的Ricci流方程 和眼眶。 所有这些主题都是研究的主流， topology. 让研究生参与到 他们的研究。 例如， 瑟斯顿是个出了名的难题。 它包含了 庞加莱猜想，它可以追溯到世纪之交。 然而，它的一部分已经成为许多博士的素材。 Thurston的学生十多年来的论文。