Let be a complex reductive linear algebraic group and let be a maximal compact subgroup. Given a nilpotent group generated by elements, we consider the representation spaces and with the natural topology induced from an embedding into and respectively. The goal of this paper is to prove that there is a strong deformation retraction of onto . We also obtain a strong deformation retraction of the geometric invariant theory quotient onto the ordinary quotient .
"The topology of nilpotent representations in reductive groups and their maximal compact subgroups." Geom. Topol. 19 (3) 1383 - 1407, 2015. https://doi.org/10.2140/gt.2015.19.1383