Mathematical Sciences: Classical Homotopy Theory

小行星9400587 F.R.科恩打算考虑的问题，在经典同伦理论和分支的其他科目涉及上同调的离散群体，某些模空间，并进一步研究了怀特海广场。 其中一个主要的项目是推广他最近的部分解决方案的M.G. Barratt有限指数猜想推广到一般情况。 他打算继续分析的群体出现在这项工作连同他们的联系与其他部分的数学涉及经典同伦理论和他们的联系，以某些模空间。 他将继续他的研究怀特黑德广场涉及相互作用之间的凯莱，迪克森代数和空间的合理职能。 F.R. Cohen和S. Gitler将继续联合工作的研究特征类空间的嵌入这是隐含在他们的早期工作，这是有关不变量的结定义的瓦西里耶夫。 这个项目是一个研究如何大尺寸的球体可以包裹在较小尺寸的物体周围，至少可以连续变形。 这种类型的几何问题在数学和其他相关领域（如物理学）中无处不在。 一些基本结构是由粒子的几何和代数结果给出的，这些粒子在表面上运动，并由时间坐标参数化。 在不同的时间，粒子可以返回到它们的原始位置。 这种几何性质的代数类似物称为挠率。 各种自然发生的空间的挠率增长的边界是这个项目的主要课题之一，这些空间是曲面的类似物。 这项工作的一个目标是攻击一个突出的问题，在被称为巴拉特的有限指数猜想的主题。 第二个意想不到的分支是，这项工作与其他一些对物理学感兴趣的人的工作重叠。 ***

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. ***