On cohomology of crystallographic groups with cyclic holonomy of split type

Details On cohomology of crystallographic groups with cyclic holonomy of split type On cohomology of crystallographic groups with cyclic holonomy of split type

2011-06-21

arxiv.org/abs/1106.4216v2

Mathematics

Algebraic Topology

13 pages

Scientific paper

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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