A Descent Theorem for Hermitian K-Theory

Abstract

Let KO and KU respectively denote the real and complex periodic K-theory spectra [1, Part III]. Let KSC denote the spectrum representing self-conjugate K-theory [2, G]. Thus we have a fibring1.1where T is induced by complex conjugation on the unitary group.The following result is due to R. Wood [1, p. 206] and, I believe, to D. W. Anderson.1.2. PROPOSITION. Let generate the stable one-stem. Then there are weak equivalences of spectraa andb