The space of commuting n-tuples in SU(2)

TL;DR

This paper characterizes the homotopy type of the suspension of the space of commuting n-tuples in SU(2) and computes its integral cohomology groups for all positive integers n.

Contribution

It provides a complete description of the homotopy type and cohomology groups of the space of commuting n-tuples in SU(2), extending understanding of its topological structure.

Findings

Homotopy type of the suspension of Y determined.

Integral cohomology groups of Y computed for all n.

Results applicable to the topology of commuting elements in SU(2).

Abstract

Let Y = Hom(Z^n, SU(2)) denote the space of commuting n-tuples in SU(2). We determine the homotopy type of the suspension of Y and compute the integral cohomology groups of Y for all positive integers n.