A spinor bundle is a vector bundle associated with the spin structure of a manifold, which allows for the description of spinor fields, mathematical objects that can represent fermionic particles in physics. This bundle provides a way to understand how spinors transform under the action of the orthogonal group, particularly in relation to the underlying geometry of the manifold. Spinor bundles are crucial in the study of noncommutative geometry as they help bridge concepts from algebra and geometry through their interactions with spectral triples.
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