Cohomology of the Space of Commuting N-tuples in a Compact Lie Group

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

On Spaces of Commuting Elements in Lie Groups

The purpose of this paper is to introduce a new method of “stabilizing” spaces of homomorphisms Hom(π,G) where π is a certain choice of finitely generated group and G is a compact Lie group. The main results apply to the space of all ordered n-tuples of pairwise commuting elements in a compact Lie group G, denoted Hom(Zn, G), by assembling these spaces into a single space for all n ≥ 0. The res...

Commuting Elements and Spaces of Homomorphisms

Abstract. This article records basic topological, as well as homological properties of the space of homomorphisms Hom(π,G) where π is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If π is a free abelian group of rank equal to n, then Hom(π,G) is the space of ordered n–tuples of commuting elements in G. If G = SU(2), a complete calculation of the cohomology of ...

Commuting Elements, Simplicial Spaces and Filtrations of Classifying Spaces

Let Γ denote the q-th stage of the descending central series of the free group on n generators Fn. For each q ≥ 2 and every topological group G, a simplicial space B∗(q, G) is constructed where Bn(q, G) = Hom(Fn/Γ , G) and the realizations B(q, G) = |B∗(q, G)| filter the classifying space BG. In particular for q = 2 this yields a single space B(2, G) assembled from all the n–tuples of commuting...

On continuous cohomology of locally compact Abelian groups and bilinear maps

Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...