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arXiv · 0710.5398

Characteristic varieties of nilpotent groups and applications

Anca Macinic·Stefan Papadima
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Abstract

We compute the characteristic varieties and the Alexander polynomial of a finitely generated nilpotent group. We show that the first characteristic variety may be used to detect nilpotence. We use the Alexander polynomial to deduce that the only torsion-free, finitely generated nilpotent groups with positive deficiency are $\Z$ and $\Z^2$, extending a classical result on nilpotent link groups.

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Anca Macinic, Stefan Papadima. 2007-10-29. Characteristic varieties of nilpotent groups and applications. https://arxiv.org/abs/0710.5398

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