classifying map

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• Classifying space — In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space for which all its homotopy groups are trivial) by a free action of G. It… …   Wikipedia

• Classifying space for U(n) — In mathematics, the classifying space for the unitary group U(n) is a space B(U(n)) together with a universal bundle E(U(n)) such that any hermitian bundle on a paracompact space X is the pull back of E by a map X → B unique up to homotopy. This… …   Wikipedia

• Clutching construction — In topology, a branch of mathematics, the clutching construction is a way of constructing fiber bundles, particularly vector bundles on spheres. Contents 1 Definition 1.1 Generalization 1.2 Classifying map construction …   Wikipedia

• Line bundle — In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising… …   Wikipedia

• Reduction of the structure group — In mathematics, in particular the theory of principal bundles, one can ask if a G bundle comes from a subgroup H < G. This is called reduction of the structure group (to H), and makes sense for any map H o G, which need not be an inclusion… …   Wikipedia

• Stable normal bundle — In surgery theory, a branch of mathematics, the stable normal bundle of a differentiable manifold is an invariant which encodes the stable normal (dually, tangential) data. It is also called the Spivak normal bundle, after Michael Spivak… …   Wikipedia

• U.S. Route 12 in Washington — This article is about the section of U.S. Route 12 in Washington. For the entire length of the highway, see U.S. Route 12. U.S. Route 12 US 12 hi …   Wikipedia

• Covering space — A covering map satisfies the local triviality condition. Intuitively, such maps locally project a stack of pancakes above an open region, U, onto U. In mathematics, more specifically algebraic topology, a covering map is a continuous surjective… …   Wikipedia

• Nerve (category theory) — In category theory, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C …   Wikipedia

• Biome — The planet Earth Biomes are climatically and geographically defined as similar climatic conditions on the Earth, such as communities of plants, animals, and soil organisms,[1] and are of …   Wikipedia

• Universal bundle — In mathematics, the universal bundle in the theory of fiber bundles with structure group a given topological group G , is a specific bundle over a classifying space BG , such that every bundle with the given structure group G over M is a pullback …   Wikipedia