spin manifold

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• Spin structure — In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical …   Wikipedia

• Spin foam — In physics, a spin foam is a topological structure made out of two dimensional faces that represents one of the configurations that must be summed to obtain a Feynman s path integral (functional integration) description of quantum gravity. It is… …   Wikipedia

• Spin network — In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum physics. From a mathematical perspective, the diagrams are a concise way to represent multilinear… …   Wikipedia

• Spin(7)-manifold — In mathematics, a Spin(7) manifold is an eight dimensional Riemannian manifold with the exceptional holonomy group Spin(7). Spin(7) manifolds are Ricci flat and admit a parallel spinor. They also admit a parallel 4 form which is a calibrating… …   Wikipedia

• G2 manifold — A G 2 manifold is a seven dimensional Riemannian manifold with holonomy group G 2. The group G 2 is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper… …   Wikipedia

• Sasakian manifold — In differential geometry, a Sasakian manifold is a contact manifold (M, heta) equipped with a special kind of Riemannian metric g, called a Sasakian metric.DefinitionA Sasakian metric is defined using the construction of the Riemannian cone .… …   Wikipedia

• Intersection form (4-manifold) — In mathematics, the intersection form of an oriented compact 4 manifold is a special symmetric bilinear form on the 2nd cohomology group of the 4 manifold. It reflects much of the topology of the 4 manifolds, including information on the… …   Wikipedia

• Complex spin structure — In mathematics a complex spin group Spin C ( n ) is a generalized form of a spin group. Although not all manifolds admit a spin group, all 4 manifolds admit a complex spin group.Scorpan, A., 2005 The Wild World of 4 Manifolds] The complex spin… …   Wikipedia

• Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …   Wikipedia

• Rokhlin's theorem — In 4 dimensional topology, a branch of mathematics, Rokhlin s theorem states that if a smooth, compact 4 manifold M has a spin structure (or, equivalently, the second Stiefel Whitney class w 2( M ) vanishes), then the signature of its… …   Wikipedia

• Clifford analysis — Clifford analysis, using Clifford algebras named after William Kingdon Clifford, is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators include, but… …   Wikipedia