Title:      The Euler class of a Poincar\'e duality group 

Author:     Ian J Leary 

Address:    Faculty of Math. Studies, Univ. of Southampton, 
            Southampton SO17 1BJ 

Abstract: The Euler class of a group $G$ of type FP over a ring $R$ 
is the element of $K_0(RG)$ given by the alternating sum of the 
modules in a finite projective resolution for $R$ over $RG$.  (We 
reserve the term "Wall obstruction" for the image of the Euler class 
in the reduced $K$-group.)  

Under an extra hypothesis satisfied in every known case, we show that 
the Euler class of an orientable odd-dimensional Poincare duality 
group over any ring has order at most two.  We construct groups that 
are of type FL over the complex numbers but are not FL over the 
rationals.  We construct group algebras over fields for which 
$K_0$ contains torsion, and construct non-free stably-free modules 
for the group algebras of certain virtually-free groups.  


Submitted.