Abstract
Let $Y := \operatorname{Hom}(\mathbb{Z}^n, \operatorname{SU}(2))$ denote the space of commuting $n$-tuples in $\operatorname{SU}(2)$. We determine the homotopy type of the suspension $\Sigma Y$, and compute the integral cohomology groups of $Y$ for all positive integers $n$.
Citation
Thomas Baird. Lisa C. Jeffrey. Paul Selick. "The space of commuting n-tuples in SU(2)." Illinois J. Math. 55 (3) 805 - 813, Fall 2011. https://doi.org/10.1215/ijm/1369841785
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