• Corpus ID: 16246240

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. 
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