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The object of this paper is to compute H∗(ΩSU(n);Z/(p)) and the Morava K–theory K(m)∗(ΩSU(n)). SU(n) as usual denotes the group of n×n unitary complex matrices with determinant one. The methods we describe will also work for the spaces ΩSU(n + 1)/SU(k) for any k ≤ n, but we will leave these questions for the interested reader. We will now state our main results. First we recover a theorem due to Waggoner [Wag85] and Yamaguchi [Yam86].

The homology and Morava K-theory of Ω 2 SU(n)