topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, i.e. continuous pointed maps from...
4 KB (597 words) - 12:21, 26 June 2024
of quantum space. Research has evolved in two directions: the more traditional canonical loop quantum gravity, and the newer covariant loop quantum gravity...
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describes the twofold loop space, Ω 2 B U {\displaystyle \Omega ^{2}BU} of BU. Here, Ω {\displaystyle \Omega } is the loop space functor, right adjoint...
13 KB (1,836 words) - 15:27, 3 May 2024
identification of 0 with 1. The set of all loops in X forms a space called the loop space of X. Free loop Loop group Loop space Loop algebra Fundamental group Quasigroup...
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Suspension (topology) (redirect from Suspension of a space)
{\displaystyle X} a loop in Y {\displaystyle Y} (an element of the loop space Ω Y {\displaystyle \Omega Y} ), and the trivial loop should be associated...
7 KB (1,245 words) - 20:39, 20 August 2024
G.} The space LG is called the free loop group on G. A loop group is any subgroup of the free loop group LG. An important example of a loop group is...
4 KB (568 words) - 01:58, 8 January 2024
Fundamental group (section Loop space)
fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about...
53 KB (8,076 words) - 07:10, 6 August 2024
homotopy (in a nice way), an infinite loop space machine produces a group completion of X together with infinite loop space structure. For example, one can...
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launching humans for space tourism, space exploration and space colonization, and provides a relatively low 3g acceleration. Launch loops were described by...
18 KB (2,538 words) - 15:32, 2 May 2024
distinguished point. Formally, let X {\displaystyle X} be a topological space. Then a free loop in X {\displaystyle X} is an equivalence class of continuous functions...
2 KB (250 words) - 21:38, 9 March 2024