## Clifford modules, finite-dimensional approximation and twisted $K$-theory

J. Math. Sci. Univ. Tokyo
Vol. 19 (2012), No. 4, Page 587–612.

Gomi, Kiyonori
Clifford modules, finite-dimensional approximation and twisted $K$-theory
A twisted version of Furuta's generalized vector bundle provides a finite-dimensional model of twisted $K$-theory. We generalize this fact involving actions of Clifford algebras. As an application, we show that an analogy of the Atiyah-Singer map for the generalized vector bundles is bijective. Furthermore, a finite-dimensional model of twisted $K$-theory with coefficients $\Z/p$ is given.