Workshop on Nil Phenomena in Topology

Vanderbilt University, Nashville TN

Investigators

Abstract

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