relative homotopy

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• 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

• 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

• Hurewicz theorem — In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier… …   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

• Crossed module — In mathematics, and especially in homotopy theory, a crossed module consists of groups G and H, where G acts on H (which we will write on the left), and a homomorphism of groups that is equivariant with respect to the conjugation action of G on… …   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

• 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

• Singular homology — In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of a… …   Wikipedia

• Floer homology — is a mathematical tool used in the study of symplectic geometry and low dimensional topology. First introduced by Andreas Floer in his proof of the Arnold conjecture in symplectic geometry, Floer homology is a novel homology theory arising as an… …   Wikipedia

• Classification of manifolds — In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Contents 1 Main themes 1.1 Overview 1.2 Different categories and additional… …   Wikipedia