homotopy decomposition

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• Homotopy groups of spheres — In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure… …   Wikipedia

• Polar decomposition — In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z where r is the absolute value of z (a… …   Wikipedia

• JSJ decomposition — In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: Irreducible orientable closed (i.e., compact and without boundary) 3 manifolds have a unique (up to isotopy)… …   Wikipedia

• CW complex — In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still… …   Wikipedia

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• Surgery theory — In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a controlled way, introduced by Milnor (1961). Surgery refers to cutting out parts of the manifold… …   Wikipedia

• Mayer–Vietoris sequence — In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to… …   Wikipedia

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• Computational topology — Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its …   Wikipedia

• Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …   Wikipedia

• Maximal compact subgroup — In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal compact subgroups play an important role in the classification of …   Wikipedia