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# deformation-retract

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• Deformation retract — Retract redirects here. For other meanings including concepts in group theory and category theory, see Retraction (disambiguation). In topology, a branch of mathematics, a retraction [1], as the name suggests, retracts an entire space into a… …   Wikipedia

• deformation retract — 1. noun A subspace such that there is a retraction onto it of the ambient space homotopic to the identity function on the ambient space. 2. verb To ha …   Wiktionary

• Deformation (engineering) — This article is about deformation in engineering. For a more rigorous treatment, see Deformation (mechanics). Compressive stress results in deformation which shortens the object but also expands it outwards. In materials science, deformation is a …   Wikipedia

• Équivalence d'homotopie — En mathématiques, une équivalence d homotopie est une application admettant une réciproque à homotopie près. Autrement dit, deux applications sont des équivalences d homotopie réciproques si leurs composées sont homotopes à l identité sur leurs… …   Wikipédia en Français

• 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

• Mapping cylinder — In mathematics, specifically algebraic topology, the mapping cylinder of a function f between topological spaces X and Y is the quotient where the union is disjoint, and ∼ is the equivalence relation That is, the mapping cylinder Mf …   Wikipedia

• Retraction (disambiguation) — A retraction is a public statement made to correct a previously made statement that was incorrect, invalid, or in error.Retraction may also refer to * Deformation retract or absolute retract, subjects in mathematical topology * Retract (category… …   Wikipedia

• Diffeomorphism — In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. The image of a… …   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

• Volume form — In mathematics, a volume form is a nowhere zero differential n form on an n manifold. Every volume form defines a measure on the manifold, and thus a means to calculate volumes in a generalized sense. A manifold has a volume form if and only if… …   Wikipedia