Let G be a complex reductive linear algebraic group and let K⊂ G be a maximal compact
subgroup. Given a nilpotent group Γ generated by r elements, we consider the …

In this paper, we study homological stability for spaces of pairwise commuting-tuples in a Lie
group. We prove that for each, these spaces satisfy rational homological stability as ranges …

In this article we study the homology of spaces Hom (\mathbb Z^ n, G) Hom (Z n, G) of
ordered pairwise commuting n-tuples in a Lie group G. We give an explicit formula for the …

For any compact, connected Lie group G and any finitely generated nilpotent group Γ, we
determine the cohomology of the path component of the trivial representation of the group …

Let $\pi $ be a discrete group, and let $ G $ be a compact connected Lie group. $\mathrm
{Hom}(\pi, G) _0 $ denotes the null-component of the space of homomorphisms from $\pi …

Let $ Hom^ 0 (\Gamma, G) $ be the path-connected component of the identity representation
of the variety of representations of a finitely generated nilpotent group $\Gamma $ into a …

Abstract Let\(\textsf {Hom}^{0}(\Gamma, G)\) be the connected component of the identity of
the variety of representations of a finitely generated nilpotent group\(\Gamma\) into a …

Let $\pi $ be a discrete group, and let $ G $ be a compact-connected Lie group. Then, there
is a map $\Theta\colon\mathrm {Hom}(\pi, G) _0\to\mathrm {map} _*(B\pi, BG) _0 $ between …

Torsion in the space of commuting elements in a Lie group Page 1 Canad. J. Math. Vol. 76 (3),
2024 pp. 1033–1061 http://dx.doi.org/10.4153/S0008414X23000317 © The Author(s), 2023 …

In this article we study the homology of spaces of homomorphisms from finitely generated
nilpotent groups to Lie groups. Of particular interest are the space of ordered pairwise …