Mathematical Sciences: Classical Homotopy Theory

数学科学：经典同伦理论

• 批准号: 9400587
• 负责人: Frederick Cohen
• 金额: $ 18万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400587&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Classical; Homotopy; Theory

9400587 Cohen F.R. Cohen intends to consider problems in classical homotopy theory and offshoots to other subjects involving cohomology of discrete groups, certain moduli spaces, and a further study of the Whitehead square. One of the main projects is to extend his recent partial solution of M.G. Barratt's finite exponent conjecture to the general case. He intends to continue an analysis of the groups appearing in this work together with their connections with other parts of mathematics involving classical homotopy theory and their connections to certain moduli spaces. He will continue his study of the Whitehead square involving an interplay between Cayley-Dickson algebras and spaces of rational functions. F.R. Cohen and S. Gitler will continue joint work in a study of characteristic classes for spaces of embeddings which are implicit in their earlier work and which are related to invariants of knots defined by Vassiliev. This project is a study of how large dimensional spheres can be wrapped around smaller dimensional objects at least up to continuous deformations. This type of geometric problem occurs ubiquitously in mathematics and other related areas such as physics. Some of the basic structure is given by the geometric and algebraic consequences of particles which move on a surface and which are parametrized by a time coordinate. At various times, the particles may return to their original position. The algebraic analogue of this geometric property is known as torsion. Bounds on the growth of torsion for various naturally occurring spaces which are analogues of surfaces is one of the main subjects of this project. One goal of this work is an attack on an outstanding problem in the subject known as Barratt's finite exponent conjecture. A second and unexpected offshoot is that this work overlaps with work of some others who are interested in physics. ***

9400587科恩·F·R·科恩打算考虑经典同伦理论中的问题及其分支，涉及离散群的上同调，某些模空间，以及进一步研究怀特黑德平方。其中一个主要项目是将他最近对M.G.Barratt的有限指数猜想的部分解推广到一般情况。他打算继续分析这部作品中出现的群，以及它们与数学的其他部分的联系，涉及经典同伦理论，以及它们与某些模空间的联系。他将继续研究涉及Cayley-Dickson代数和有理函数空间之间相互作用的怀特黑德正方形。F.R.Cohen和S.Gitler将继续共同研究嵌入空间的特征类，这些特征类在他们早期的工作中是隐含的，并且与Vassiliev定义的纽结的不变量有关。这个项目是研究如何将大维度的球体包裹在较小维度的物体周围，至少达到连续变形。这种类型的几何问题在数学和其他相关领域如物理中普遍存在。一些基本结构是由在曲面上运动的粒子的几何和代数结果给出的，这些粒子由时间坐标参数化。在不同的时间，粒子可能会回到它们原来的位置。这种几何性质的代数模拟称为扭转。各种类似于曲面的自然空间的挠率增长的界是这个项目的主要主题之一。这项工作的一个目标是攻击该学科中的一个突出问题，即巴拉特有限指数猜想。第二个出乎意料的分支是，这项工作与其他一些对物理感兴趣的人的工作重叠。***