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Let us consider topological complex K-theory as the cohomology theory represented by the spectrum <math>KU</math>. In this case, <math>KU^*(BU(n))\cong \mathbb{Z}[t,t^{-1}][[c_1,...,c_n]]</math><ref> Adams 1974, p. 49</ref>, and <math> KU_*(BU(n))</math> is the free <math>\mathbb{Z}[t,t^{-1}]</math> module on <math>\beta_0</math> and <math>\beta_{i_1}\ldots\beta_{i_r}</math> for <math>n\geq i_j > 0</math> and <math>r\leq n</math>.<ref> Adams 1974, p. 47</ref>
{{warning|The description of the K-theory of BU(n) below is incomplete, and unclear. The author of the secion below should clarify what they are computing. It seems more like a computation of <math>KU_*KU</math.>}}
The [[topological K-theory]] is known explicitly in terms of [[numerical polynomial|numerical]] [[symmetric polynomial]]s.
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