國立清華大學 數學系

Abstract

Complex connective K-theory is represented by the spectrum bu, which is related to the classifying space of the infinite unitary group. Determining the stable splitting of the spectra bu^X for a space X will give rise to the structure of the bu-homology of X. In this talk we show that the mod 2 cohomology of bu^BSO(2n) is isomorphic to a direct sum of E-modules, E=Z/2<Q(0),Q(1)>. This would give the algebraic splitting of the complex connective K-theory of BSO(2n). Although the full topological splitting cannot be obtained yet due to the complexity of the modules, it nevertheless still gives certain information about the properties of bu^BSO(2n).