spin manifold
1Spin 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 …
2Spin 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… …
3Spin 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… …
4Spin(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… …
5G2 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… …
6Sasakian 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 .… …
7Intersection 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… …
8Complex 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… …
9Holonomy — 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… …
10Rokhlin'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… …
