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5 votes
0 answers
255 views

Necessity of Banach category for K-theory

In Karoubi's book on K-Theory (K-Theory, An Introduction), he introduces the groups $K^{p,q}(C)$ for a pseudo-abelian Banach category $C$. My question is whether the requirement that $C$ be a Banach ...
3 votes
0 answers
491 views

What is the Atiyah-Bott-Shapiro map for a bundle of *complex* quadratic forms?

In order to ask the question in the title more precisely, let me recall some standard stuff introduced in [1; Atiyah, Bott, Shapiro]. Suppose $X$ is a compact CW complex and $V \to X$ is an oriented ...