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

9313048达弗曼在拓扑流形的识别问题上做了大量的工作。这就是找到有效的标准来区分流形和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判据，但即使当这种判据失败并且描述几何对象的函数具有奇异性时，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Cannon-Edwards定理，该定理认为同调球面的双重悬挂是一个球面。1978年，Cannon提出了一套识别高维拓扑流形的简单准则。1991年，科比、费里、米奥和温伯格证明了加农的标准是不够的。事实上，他们构造了无限多个不同的“非笛卡尔流形”族--满足Cannon标准的、没有局部坐标描述的类似流形的物体。这些空间的详细几何形状是神秘的。拟议的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学以及数学和数学物理的其他领域中的应用。这次会议将在整个美国东南部非常有吸引力，这个地区号称对这个话题有着悠久的兴趣。***

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. ***