Representation spaces for central extensions and almost commuting unitary matrices

Abstract

Let $\Gamma$ denote a central extension of the form $1\to {\mathbb{Z}}^r\to \Gamma \to {\mathbb{Z}}^n\to 1$. In this paper we describe the topology of the spaces of homomorphisms $\text{Hom}(\Gamma ,U(m))$ and the associated moduli spaces $\text{Rep}(\Gamma ,U(m))$, where $U(m)$ is the group of $m\times m$ unitary matrices.

arXiv comment23 pages. Minor typos fixed. To appear in the Journal of the London Mathematical Society

References in corpus (3)

• Cohomology of the space of commuting n-tuples in a compact Lie group
• The topology of nilpotent representations in reductive groups and their maximal compact subgroups
• Stable splittings, spaces of representations and almost commuting elements in Lie groups

Cited by in corpus (2)

• Deformations of nilpotent groups and homotopy symmetric $C^{\ast }$-algebras
• On the moduli spaces of commuting elements in the projective unitary groups