  Let $\Gamma$ be a finitely generated nilpotent group and let G be a complex
reductive algebraic group. The representation variety $\mathrm{Hom}(\Gamma,G)$
and the character variety $\mathrm{Hom}(\Gamma,G)//G$ each carry a natural
topology, and we describe the topology of their connected components in terms
of representations factoring through quotients of $\Gamma$ by elements of its
lower central series.
