Illinois Journal of Mathematics

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

Thomas Baird, Lisa C. Jeffrey, and Paul Selick

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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 $n$.

Article information

Illinois J. Math., Volume 55, Number 3 (2011), 805-813.

First available in Project Euclid: 29 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
Secondary: 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms


Baird, Thomas; Jeffrey, Lisa C.; Selick, Paul. The space of commuting n -tuples in SU(2). Illinois J. Math. 55 (2011), no. 3, 805--813. doi:10.1215/ijm/1369841785.

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