Witt Groups of Complex Cellular Varieties

Abstract

We show that the Grothendieck-Witt and Witt groups of smooth complex cellular varieties can be identified with their topological KO-groups. As an application, we deduce the values of the Witt groups of all irreducible hermitian symmetric spaces, including smooth complex quadrics, spinor varieties and symplectic Grassmannians. 2010 Mathematics Subject Classification: Primary 11E81; Secondary 19G99, 19L99, 32M15