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homotopic complex

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  • Chain complex — Bicomplex redirects here. For the number, see Bicomplex number In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between …   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 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

  • Topicity — Main article: stereochemistry In chemistry, topicity is the stereochemical relationship of substituents relative to the structure to which they are attached. Depending on the relationship, such groups can be heterotopic, homotopic, enantiotopic,… …   Wikipedia

  • Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

  • Contractibility of unit sphere in Hilbert space — In topology, it is a surprising fact that the unit sphere in (infinite dimensional) Hilbert space is a contractible space, sinceno finite dimensional spheres are contractible.This can be demonstrated in several different ways. Topological proof… …   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

  • Normal invariant — In mathematics, a normal map is a concept in geometric topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X, a normal map on X endows the space, roughly speaking, with some of the… …   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

  • Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   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

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