Title:      On algebraic and geometric dimensions for groups with torsion  

Authors:    Noel Brady, Ian J. Leary and Brita E. A. Nucinkis 

Addresses:  N Brady:  Dept. of Math., Univ. of Oklahoma, Norman OK 73019, 

            I Leary:  Fac. of Math. Studies, Univ. of Southampton,
                      Southampton SO17 1BJ 

         B Nucinkis:  Departement Mathematik, ETH Z\"urich, CH8092,
                      Z\"urich.  

Abstract: We argue that the geometric dimension of a discrete group $G$
ought to be defined to be the minimal dimension of a model for the 
universal proper $G$-space rather than the minimal dimension of a
model for the universal free $G$-space.  For torsion-free groups, 
these two quantities are equal, but the new quantity can be finite 
for groups containing torsion whereas the old one cannot.  There 
is an analogue of cohomological dimension (defined in terms of Bredon
cohomology) for which analogues of the Eilenberg-Ganea and
Stalling-Swan theorems (due to W. Lueck and M. J. Dunwoody
respectively) hold.  We show that some groups constructed by
M. Bestvina and M. Davis provide counterexamples to the analogue of
the Eilenberg-Ganea conjecture.   

Submitted.  

PS: There is a Postscript picture, not in the dvi file.  It consists 
of a regular pentagon, divided into 5 equal triangles, with each 
triangle divided into 4 smaller triangles with the same angles as 
the big ones.