This talk is part of the following reading seminar: Seiberg-Witten theory (Fall 2025).

Abstract

During the last talk, we were introduced to the spin and spin^c group and its representation. In the 3rd talk of the Seiberg-Witten seminar, we will go from this linear algebra picture to the case of bundles. Specifically, we will focus on obstructions to the existence of spin and spin^c structure on manifolds. From this, we will see that all simply connected 4-manifold admit a spin^c structure. Finally, we will introduce spinors. Along the way, we will cover plenty of examples.