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

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

2011-05-24

arxiv.org/abs/1105.4772v1

Mathematics

Algebraic Topology

27 pages

Scientific paper

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.

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