loop homotopy

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• Loop space — In mathematics, the space of loops or (free) loop space of a topological space X is the space of loops from the unit circle S 1 to X together with the compact open topology. :Omega X = mathcal{C}(S^1, X).That is, a particular function space. In… …   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

• 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

• Loop group — In mathematics, a loop group is a group of loops in a topological group G with multiplication defined pointwise. Specifically, let LG denote the space of continuous maps S^1 o G equipped with the compact open topology. An element of LG is called… …   Wikipedia

• Loop braid group — The loop braid group is a mathematical group structure that is used in some models of theoretical physics to model the exchange of particles with loop like topologies within three dimensions of space and time.The basic operations which generate a …   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

• Free loop — In the mathematical field of topology, a free loop is a variant of the mathematical notion of a loop. Whereas a loop has a distinguished point on it, called a basepoint, a free loop lacks such a distinguished point. Formally, let X be a… …   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

• Bott periodicity theorem — In mathematics, the Bott periodicity theorem is a result from homotopy theory discovered by Raoul Bott during the latter part of the 1950s, which proved to be of foundational significance for much further research, in particular in K theory of… …   Wikipedia

• Orthogonal group — Group theory Group theory …   Wikipedia