spin geometry, string geometry, fivebrane geometry …
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
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 $q$ and the quotient of Clifford modules of rank $q$ by those that have an extension to Clifford modules of rank $q+1$.
The generalization of this to Clifford module bundles is the content of Karoubi K-theory.
The orginal reference is
The result is reviewed as theorem I 9.27 in
Created on November 24, 2014 at 12:45:14. See the history of this page for a list of all contributions to it.