Topological proof of Bott periodicity and characterization of BR (Q2497081)

M. F. Atiyah defined \(KR\)-theory as the Grothendieck group of the monoid of real vector bundles. \(KR\)-theory is known to be representable with classifying space \(BR\) which is the real space \(BU\) with involution the conjugation of \(BU\). The \(\mathbb{Z}_2\)-equivariant periodicity of \(BR\) is called the \((1,1)\)-periodicity. The purpose of this paper is to give another proof of the \((1,1)\)-periodicity of \(BR\) and to characterize \(BR\) in a topological way. This is a generalization of a result concerning \(BU\) which was obtained by K. Kono and K. Tokumaga in 1994.