On the group cohomology of the semi-direct product Z^n rtimes Z/m and a conjecture of Adem-Ge-Pan-Petrosyan

Abstract

Consider the semi-direct product Z^n rtimes Z/m. A conjecture of Adem-Ge-Pan-Petrosyan predicts that the associated Lyndon-Hochschild-Serre spectral sequence collapses. We prove this conjecture provided that the Z/m-action on Z^n is free outside the origin. We disprove the conjecture in general, namely, we give an example with n=6 and m=4, where the second differential does not vanish.

27 pages

References in corpus (2)

• On the classifying space of the family of virtually cyclic subgroups
• C*-algebras associated with integral domains and crossed products by actions on adele spaces