Workshop on Nil Phenomena in Topology

这是一份为参加“拓扑零现象”研讨会提供住宿和旅费的提案，该研讨会将于2007年4月14日至15日在范德比尔特大学（美国田纳西州纳什维尔）举行。大约有20位拓扑学家受邀参加，他们目前的工作几乎都与研讨会的主题有关。讲习班的目的是让已有经验的专家和较年轻的研究人员参与讨论目前的情况和未来研究的可能性。研讨会的主题是计算和处理被称为Nil和UNil的神秘代数结构，这是35年前由Friedhelm Waldhausen和Sylvain Cappell定义的。在代数上，这些结构是K-和l-理论中Mayer-Vietoris型序列的修正项，它们与Farrell-Jones同构猜想有很强的联系。在几何上，这些结构阻碍了流形之间沿双侧子流形的同伦等价的分裂，这与等变Borel猜想有很强的联系。因此，这些阻碍群在高维流形几何拓扑的约简问题中起着中心作用。研讨会的目的是将过去35年来出现的“零现象”的各个分支学科联系起来，这是及时的。值得在这次会议上宣传的观点是范畴论、操纵论、微分几何论和控制拓扑论。除了对全局的普遍认识之外，我们还希望在从理论结构到代数计算再到流形拓扑中的几何结果的“装配线”中激发更多的协作。更多信息可在会议主页http://www.math.vanderbilt.edu/~hughescb/Nil07.htm上找到

This is a proposal to provide funding for lodging and travel to the workshop "Nil Phenomena in Topology," which will be held at Vanderbilt University (Nashville, Tennessee USA) on 14-15 April 2007. Approximately 20 topologists are invited to participate, almost all of whose current work is related to the theme of the workshop. The purpose of the workshop is to engage established experts and younger researchers in discussions on the current state of affairs and on possibilities for future research. The theme of the workshop is the calculation and handling of mysterious algebraic structures called Nil and UNil, defined 35 years ago by Friedhelm Waldhausen and Sylvain Cappell. Algebraically, these structures are the correction terms to Mayer-Vietoris type sequences in K- and L-theory, which have a strong connection to the Farrell-Jones Isomorphism Conjecture. Geometrically, these structures obstruct the splitting of homotopy equivalences between manifolds along two-sided sub-manifolds, which has a strong connection to the Equivariant Borel Conjecture. Therefore these obstruction groups play a central role in the reduction problem in the geometric topology of high-dimensional manifolds.The workshop is timely in that it aims to connect the various sub-disciplines of the "Nil phenomena" that have emerged in the past 35 years. The points of view that merit publicity at this gathering are the categorical, the manipulative, the differential-geometric, and the controlled-topological. Besides a general awareness of the big picture, we would like to stimulate more collaboration in the "assembly line" from theoretical structure to algebraic computations to geometric consequences in the topology of manifolds. More information can be found on the conference homepage http://www.math.vanderbilt.edu/~hughescb/Nil07.htm