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Spring Topology and Dynamical Systems Conference 2003
March 20-22, 2003
Texas Tech University
Lubbock, TX, USA

Organizers
Wayne Lewis, Razvan Gelca, Harold Bennett, Carl Seaquist

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L2-cohomology of Coxeter groups, Hecke algebras and buildings
by
Michael Davis
The Ohio State University
Coauthors: Jan Dymara, Tadeusz Januszkiewicz, Boris Okun

The reduced L2-cohomology of the universal cover of a CW complex or of a manifold lies somewhere between its ordinary cohomology and its cohomology with compact supports. One of the most interesting interpretations of the previous sentence comes from the study of the L2-cohomology of buildings. (Here we are concerned with the buildings associated to general Coxeter groups not just spherical or Euclidean reflection groups.) A related interpretation comes from the Singer Conjecture - that the reduced L2-cohomology of the universal cover of an aspherical manifold vanishes except in the middle dimension. I will discuss work on these two topics by Dymara, Januszkiewicz, Okun and myself.

Date received: January 24, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajz-09.