English

A descent theorem in topological K-theory

K-Theory and Homology 2007-05-23 v1 Operator Algebras

Abstract

Let A be a Banach algebra and A' its complexification. In this paper we show that the homotopy fixed point set of K(A'), the topological K-theory space of A', under complex conjugation is just K(A), the topological K-theory space of A. This result generalizes the well known fact that BO is BU^hZ/2. The proof uses in an essential way Atiyah's KR theory and the Clifford algebra definition of higher K-groups.

Keywords

Cite

@article{arxiv.math/0509396,
  title  = {A descent theorem in topological K-theory},
  author = {Max Karoubi},
  journal= {arXiv preprint arXiv:math/0509396},
  year   = {2007}
}

Comments

5 pages ; see also http://www.math.jussieu.fr/~karoubi/