On the Exponent of Cohomology of Discrete Groups

In sufficiently high dimensions, Farrell cohomology coincides with ordinary cohomology. The torsion occurring asymptotically often arises from the finite subgroups in a simple way, but our example shows that a different type of cohomological twisting can appear, linked to the geometry of the singular set of the (j-complex X/V. We obtain a general bound on the exponent of H*(T, Z) by combining the description given previously with a recent result on torsion in equivariant cohomology: