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Diffgeom β

Spin structure

Definition

A spin structure on an oriented Riemannian manifold is a lift of its gluing cocycle to SO(n), to a gluing cocycle to Spin(n), the double cover of SO(n).

Two spin structures are said to be equivalent if Fill this in later

The set of isomorphism classes of spin structures on a Riemannian manifold M is denoted as Spin(M).