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In differential geometry, a metaplectic structure is the symplectic analog of spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic manifold allows one to define the symplectic spinor bundle, which is the Hilbert space bundle associated to the metaplectic structure via the metaplectic representation, giving rise to the notion of a symplectic spinor field in differential geometry.

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rdfs:label	Metaplectic structure (en)
rdfs:comment	In differential geometry, a metaplectic structure is the symplectic analog of spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic manifold allows one to define the symplectic spinor bundle, which is the Hilbert space bundle associated to the metaplectic structure via the metaplectic representation, giving rise to the notion of a symplectic spinor field in differential geometry. (en)
dcterms:subject	Symplectic geometry Structures on manifolds Algebraic topology
Wikipage page ID	32019964 (xsd:integer)
Wikipage revision ID	1030449025 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum field theory Metaplectic group Algebraic topology Symplectic geometry Structures on manifolds Obstruction theory Symplectic spinor bundle Symplectic group Symplectic manifold Mathematical physics Algebraic topology Equivariant Riemannian manifold Hilbert space Chern class Symplectic geometry Differential geometry Spin geometry Symplectic frame bundle Stiefel-Whitney class Orientable Spin structure Springer-Verlag Covering map K theory Cohomology group
sameAs	Metaplectic structure Metaplectic structure Metaplectic structure Metaplectic structure
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Reflist
has abstract	In differential geometry, a metaplectic structure is the symplectic analog of spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic manifold allows one to define the symplectic spinor bundle, which is the Hilbert space bundle associated to the metaplectic structure via the metaplectic representation, giving rise to the notion of a symplectic spinor field in differential geometry. Symplectic spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in establishing the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for symplectic spin geometry. (en)
gold:hypernym	Analog
prov:wasDerivedFrom	wikipedia-en:Metaplectic_structure?oldid=1030449025&ns=0
page length (characters) of wiki page	5810 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Metaplectic_structure
is Link from a Wikipage to another Wikipage of	Metaplectic group Symplectic spinor bundle Symplectic frame bundle Spin structure
is foaf:primaryTopic of	wikipedia-en:Metaplectic_structure

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