n-th homotopy group

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• Homotopy group — In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The base point preserving maps from an n dimensional sphere (with base point) into a given space (with base point) are collected into equivalence… …   Wikipedia

• Size homotopy group — The concept of size homotopy group is the anologous in size theory of the classical concept of homotopy group. In order to give its definition, let us assume that a size pair (M,varphi) is given, where M is a closed manifold of class C^0 and… …   Wikipedia

• 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

• Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… …   Wikipedia

• Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

• Homotopy sphere — In algebraic topology, a branch of mathematics, a homotopy sphere is an n manifold homotopy equivalent to the n sphere. It thus has the same homotopy groups and the same homology groups, as the n sphere. So every homotopy sphere is an homology… …   Wikipedia

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

• Homotopy category — In mathematics, a homotopy category is a category whose objects are topological spaces and whose morphisms are homotopy classes of continuous functions. The homotopy category of all topological spaces is often denoted hTop or Toph.Homotopy… …   Wikipedia

• homotopy — /heuh mot euh pee, hoh /, n., pl. homotopies. Math. the relation that exists between two mappings in a topological space if one mapping can be deformed in a continuous way to make it coincide with the other. [1915 20; HOMO + topy ( < Gr tóp(os)… …   Universalium

• Homotopy category of chain complexes — In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences. It lies intermediate between the category of chain… …   Wikipedia

• Homotopy to Marie — Infobox Album Name = Homotopy to Marie Type = Album Artist = Nurse With Wound Released = 1982 Recorded = 1981 82 Genre = Industrial, Experimental Length = 65:30 Label = United Dairies Producer = Steven Stapleton Reviews = *Allmusic (3.5/5)… …   Wikipedia