Authors: Mike W Davis, Tadeusz Januszkiewicz and Ian J Leary 

Mike Davis 
Affiliation: The Ohio State University 

Tadeusz Januszkiewicz 
Affiliation: The Ohio State University 

Ian Leary 
Affiliation: The Ohio State University 

Abstract: We compute the $\ell^2$-Betti numbers of the complement 
of a finite collection of hyperplanes in the complex space $\Bbb C^n$.
At most one of the $\ell^2$-Betti numbers is non-zero.  If the 
arrangement of hyperplanes is essential (i.e., not the product of 
$\Bbb C$ with a lower-dimensional arrangement) then the $n$th 
$\ell^2$-Betti number is the one that can be non-zero.  

Status: preprint