nLab
Atiyah-Bott-Shapiro isomorphism

Contents

Context

Spin geometry

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

The Atiyah-Bott-Shapiro isomorphism (due to Atiyah-Bott-Shapiro 63) is an isomorphism between the real/complex topological K-theory ring of the point in degree qq and the quotient of Clifford modules of rank qq by those that have an extension to Clifford modules of rank q+1q+1.

The generalization of this to Clifford module bundles is the content of Karoubi K-theory.

References

The orginal reference is

The result is reviewed as theorem I 9.27 in

Created on November 24, 2014 at 12:33:04. See the history of this page for a list of all contributions to it.