Witt groups of complex cellular varieties

TL;DR

This paper establishes an isomorphism between algebraic Witt groups of smooth complex cellular varieties and their topological KO-groups, enabling explicit calculations for various symmetric spaces.

Contribution

It demonstrates the equivalence of algebraic Witt groups and topological KO-groups for smooth complex cellular varieties, providing new computational tools.

Findings

Witt groups of smooth complex cellular varieties are isomorphic to their topological KO-groups.

Explicit Witt group values are obtained for hermitian symmetric spaces, including quadrics and Grassmannians.

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.