Authors

Bartosz Putrycz, Nansen Petrosyan 


Title 

On cohomology of crystallographic groups with cyclic holonomy of split type



Abstract

We disprove a conjecture stating that the integral cohomology of any n-dimensional crystallographic group with cyclic holomony is given by  the cohomology of the holonomy group with coefficients in the cohomology of the  associated lattice subgroup. We provide a complete list of counterexamples up to dimension 6. This finishes the computations of the cohomology of 6-dimensional crystallographic groups arising as orbifold fundamental groups of certain
Calabi-Yau toroidal orbifolds. We also find a counterexample with odd order holonomy in dimension 8.

Status

2012, submitted.