Mathematical Sciences:NSF/CBMS Regional Conferences in the Math Sciences-Controlled Topology and the Characterization of Manifolds; May 24-28, 1994; Knoxville, Tennessee

小行星9313048 拓扑流形的识别问题已作了大量的努力。 这是一个寻找有效的标准来区分流形与其他更奇异的几何对象的问题。 经典的隐函数定理给出了一个这样的标准，但即使这失败了，描述几何对象的函数也有 奇点，对象本身仍然可以是流形。 这一现象的一个引人注目的例子是著名的坎农-爱德华兹定理，它说，一个同调球的双重悬挂是一个球。 1978年，Cannon提出了一套简单的判别高维拓扑流形的准则. 1991年，Bryant、Ferry、Mio和Weinberger指出Cannon的标准是不够的。 事实上，他们建造了无限多个不同的家庭“noncartuminous流形”-流形一样的对象满足坎农的标准，没有当地的坐标描述。 这些空间的几何细节是神秘的。 拟议的会议的目的是暴露这项工作的数学公众和寻求应用这些想法都在几何拓扑和其他领域的数学和数学物理。 会议将在整个美国东南部非常有吸引力，该地区拥有对该主题感兴趣的悠久传统。 ***

9313048 Daverman A good deal of effort has gone into the recognition problem for topological manifolds. This is the problem of finding effective criteria for distinguishing manifolds from other, more singular, geometric objects. The classical implicit function theorem gives one such criterion, but even when this fails and the functions describing the geometric object have singularities, the object itself may nevertheless be a manifold. A compelling example of this phenomenon is the celebrated Cannon-Edwards theorem, which says that the double suspension of an homology sphere is a sphere. In 1978, Cannon proposed a simple set of criteria for recognizing high- dimensional topological manifolds. In 1991, Bryant, Ferry, Mio, and Weinberger showed that Cannon's criteria were insufficient. In fact, they constructed infinitely many distinct families of "noncartesian manifolds" - manifold-like objects satisfying Cannon's criteria which do not have local coordinate descriptions. The detailed geometry of these spaces is mysterious. The purpose of the proposed conference is to expose this work to the mathematical public and seek applications of these ideas both within geometric topology and in other areas of mathematics and mathematical physics. The conference will be very appealing throughout the Southeastern United States, a region which boasts a long tradition of interest in the topic. ***