Speaker: 谢恒，中山大学

Inviter: 邹佛灵

Title: Clifford Modules, Spinor Bundles, and Quadratic Forms on Spheres

Language: Chinese

Time & Venue: 2026.06.08 14:30-15:30 南楼N820

Abstract: In the 1960s, Atiyah, Bott, and Shapiro used Clifford modules to construct spinor bundles on spheres. Spinor bundles represent the nontrivial generators in the real K-theory of spheres (aka. KO-theory), which underlies the Bott periodicity. In 1969, Fossum proved that the comparison map from the algebraic K-theory of spheres to their topological KO-theory is surjective, and Swan later proved that this map is in fact an isomorphism. This shows that, to some extent, algebraic and topological real vector bundles agree for spheres. In 1977, Knebusch noted that quadratic forms on vector bundles over spheres are natural objects to study. In this talk, I will give an explicit construction of quadratic forms on spinor bundles and explain how this construction suggests that algebraic vector bundles over spheres, even with quadratic forms, can still correspond to topological real vector bundles.