homotopy group of spheres

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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

• 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

• 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 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

• Orthogonal group — Group theory Group theory …   Wikipedia

• Stable homotopy theory — In mathematics, stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the… …   Wikipedia

• Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …   Wikipedia

• Spectrum (homotopy theory) — In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, all of which give the same homotopy category.Suppose we… …   Wikipedia

• Rational homotopy theory — In mathematics, rational homotopy theory is the study of the rational homotopy type of a space, which means roughly that one ignores all torsion in the homotopy groups. It was started by Dennis Sullivan (1977) and Daniel Quillen (1969) …   Wikipedia

• p-compact group — In mathematics, in particular algebraic topology, a p compact group is (roughly speaking) a space that is a homotopical version of a compact Lie group, but with all the structure concentrated at a single prime p. This concept was introduced by… …   Wikipedia

• Exotic sphere — In differential topology, a mathematical discipline, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n sphere. That is, M is a sphere from the point of view of all its… …   Wikipedia