# Characteristic varieties of nilpotent groups and applications

@article{Macinic2007CharacteristicVO, title={Characteristic varieties of nilpotent groups and applications}, author={Anca Macinic and Stefan Papadima}, journal={arXiv: Algebraic Topology}, year={2007} }

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.

## 15 Citations

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