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

对拓扑流形的识别问题已经做了大量的研究。这个问题是找到区分流形和其他更奇异的几何物体的有效准则。经典隐函数定理给出了一个这样的判据，但即使这个判据不成立，而且描述几何对象的函数有奇点，这个对象本身仍然可能是一个流形。这一现象的一个引人注目的例子是著名的卡农-爱德华兹定理，它说同调球的双悬是一个球。1978年，坎农提出了一套简单的标准来识别高维拓扑流形。1991年，Bryant、Ferry、Mio和Weinberger证明了Cannon的标准是不充分的。事实上，他们构造了无穷多个不同的“非笛卡儿流形”族——满足坎农准则的流形类物体，它们没有局部坐标描述。这些空间的详细几何结构是神秘的。本次会议的目的是向数学公众展示这项工作，并寻求这些思想在几何拓扑和其他数学和数学物理领域的应用。这次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. ***