Spinc structure
In spin geometry, a spinᶜ structure (or complex spin structure) is a special classifying map that can exist for orientable manifolds. Such manifolds are called spinᶜ manifolds. C stands for the complex numbers, which are denoted and appear in the definition of the underlying spinᶜ group. In four dimensions, a spinᶜ structure defines two complex plane bundles, which can be used to describe negative and positive chirality of spinors, for example in the Dirac equation of relativistic quantum field theory. Another central application is Seiberg–Witten theory, which uses them to study 4-manifolds.
