On cohomology of crystallographic groups with cyclic holonomy of split type
Algebraic Topology
2011-06-23 v2 Group Theory
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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Cite
@article{arxiv.1106.4216,
title = {On cohomology of crystallographic groups with cyclic holonomy of split type},
author = {Nansen Petrosyan and Bartosz Putrycz},
journal= {arXiv preprint arXiv:1106.4216},
year = {2011}
}
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13 pages