A survey on spaces of homomorphisms to Lie groups

Abstract

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation theory, as well as other structures. Various properties are given when $G$ is replaced by a small category, or the discrete group is given by a right-angled Artin group.

18 pages

References in corpus (8)

• The topology of nilpotent representations in reductive groups and their maximal compact subgroups
• A classifying space for commutativity in Lie groups
• Covering spaces of character varieties
• On the fundamental group of Hom(Z^k,G)
• On spaces of commuting elements in Lie groups
• Homotopy colimits of classifying spaces of abelian subgroups of a finite group
• On decomposing suspensions of simplicial spaces
• On monodromy representations in Denham-Suciu fibrations

Cited by in corpus (10)

• Colimits of abelian groups
• Poincare series of character varieties for nilpotent groups
• Hilbert-Poincare series for spaces of commuting elements in Lie groups
• Differentiable stratified groupoids and a de Rham theorem for inertia spaces
• On structured spaces and their properties
• Vanishing theorems for representation homology and the derived cotangent complex
• Commuting matrices and Atiyah's Real K-theory
• Polyhedral products, flag complexes and monodromy representations
• Commutative classifying space for simplicial groups
• Commutative d-Torsion K-Theory and Its Applications