Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:Riemannian_manifold |
| gptkbp:definedIn |
admitting a lift of the frame bundle to a spin group
|
| gptkbp:dimensions |
any dimension
|
| https://www.w3.org/2000/01/rdf-schema#label |
spin manifold
|
| gptkbp:isDefinedOver |
complex numbers
real numbers |
| gptkbp:relatedTo |
gptkb:Lie_group
gptkb:Atiyah-Singer_index_theorem gptkb:Stiefel-Whitney_class orthogonal group principal bundle vector bundle Dirac operator frame bundle orientable manifold Pin manifold spin cobordism spinor bundle string manifold |
| gptkbp:requires |
second Stiefel-Whitney class to vanish
|
| gptkbp:structure |
spin structure
|
| gptkbp:subspecies |
gptkb:Riemannian_manifold
oriented manifold |
| gptkbp:usedIn |
gptkb:theoretical_physics
gptkb:topology gptkb:string_theory differential geometry index theory Dirac operator theory |
| gptkbp:bfsParent |
gptkb:Riemannian_manifold
|
| gptkbp:bfsLayer |
5
|