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A Note On Nilpotent Representations (1501.04357v2)
Published 18 Jan 2015 in math.AT, math.GR, and math.RT
Abstract: 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.