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arXiv · 1106.4216

On cohomology of crystallographic groups with cyclic holonomy of split type

Nansen Petrosyan·Bartosz Putrycz
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Abstract

We disprove a conjecture stating that the integral cohomology of any crystallographic group Z^n \rtimes Z_m is given by the cohomology of Z_m with coefficients in the cohomology of the group Z^n, by providing a complete list of counterexamples up to dimension 5. We also find a counterexample with odd order holonomy, m=9, in dimension 8 and finish the computations of the cohomology of 6-dimensional crystallographic groups arising as orbifold fundamental groups of certain Calabi-Yau toroidal orbifolds.

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Nansen Petrosyan, Bartosz Putrycz. 2011-06-22. On cohomology of crystallographic groups with cyclic holonomy of split type. https://arxiv.org/abs/1106.4216

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