Flawed groups and the topology of character varieties

A finitely presented group Gamma is called flawed if Hom(Gamma, G) /G deformation retracts onto its subspace Hom(Gamma, K)/K for all reductive affine algebraic groups G and maximal compact subgroups K subset of G. After discussing generalities concerning flawed groups, we show that all finitely generated groups isomorphic to a free product of nilpotent groups are flawed. This unifies and generalizes all previously known classes of flawed groups. We also provide further evidence for the authors' conjecture that RAAGs are flawed. Lastly, we show direct products between finite groups and some flawed group are also flawed. These latter two theorems enlarge the known class of flawed groups.

Automated summary

This paper discusses the general properties of flawed groups, proves that all finitely generated groups isomorphic to a free product of nilpotent groups are flawed, and provides further evidence for the conjecture that RAAGs are flawed. The paper also shows that direct products between finite groups and some flawed groups are also flawed.