A descent theorem in topological K-theory

Details A descent theorem in topological K-theory A descent theorem in topological K-theory

2005-09-18

arxiv.org/abs/math/0509396v1

K-theory 24, p. 109-114 (2001)

Mathematics

K-Theory and Homology

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

Scientific paper

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.

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