Title:      The $L^2$-cohomology of Artin groups 

Authors:    Michael W. Davis and Ian J. Leary

Addresses:  

M. W. Davis
Department of Mathematics
The Ohio State University
231 W. 18th Avenue
Columbus
Ohio 43210
United States

I. J. Leary 
Faculty of Mathematical Studies
University of Southampton
Southampton
SO17 1BJ
United Kingdom

Abstract:  For each Artin group we compute the reduced $L^2$-cohomology
of (the universal cover of) its ``Salvetti complex''. This is a
CW-complex which is conjectured to be a model for the classifying
space of the Artin group. In the many cases when this conjecture is
known to hold our calculation describes the reduced $L^2$-cohomology of
the Artin group.  

The calculation is surprising for two reasons: firstly, the fact that
it can be done at all (whereas for example the ordinary rational
cohomology of every Artin group is not known) and secondly because the
answer is highly non-trivial (many other calculations of $L^2$-cohomology
groups have used vanishing theorems to show that all or most of these
groups are zero).