# Spin structure

From Diffgeom

(Redirected from Spin manifold)

## Definition

A **spin structure** on an oriented Riemannian manifold is a lift of its gluing cocycle to , to a gluing cocycle to , the double cover of .

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 is denoted as .