Homotopy Groups

Some articles on homotopy, groups, homotopy groups, group, homotopy group:

Rational Homotopy Theory - The Sullivan Minimal Model of A Topological Space
... model as APL(X) is called a model for the space X, and determines the rational homotopy type of X when X is simply connected ... To any simply connected CW complex X with all rational homology groups of finite dimension one can assign a minimal Sullivan algebra ΛV of APL(X), which has the property ... This gives an equivalence between rational homotopy types of such spaces and such algebras, such that The rational cohomology of the space is the cohomology of its Sullivan minimal model ...
Homotopy Groups Of Spheres - General Theory - Ring Structure
... The direct sum of the stable homotopy groups of spheres is a supercommutative graded ring, where multiplication is given by composition of representing maps, and any element of non-zero degree is ... generator of π3S, while η4 is zero because the group π4S is trivial ... The Toda bracket is not quite an element of a stable homotopy group, because it is only defined up to addition of products of certain other elements ...
Stable Homotopy Theory
... In mathematics, stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications ... states that for a given CW-complex X the (n+i)th homotopy group of its ith iterated suspension, πn+i (ΣiX), becomes stable (i.e ... In the two examples above all the maps between homotopy groups are applications of the suspension functor ...
Projective Unitary Group - The Topology of PU(H) - The Homotopy and (co)homology of PU(H)
... In particular, using the isomorphism between the homotopy groups of a space X and the homotopy groups of its classifying space BX, combined with the homotopy ... As a consequence, PU must be of the same homotopy type as the infinite-dimensional complex projective space, which also represents K(Z,2) ... they have isomorphic homology and cohomology groups H2n(PU)=H2n(PU)=Z and H2n+1(PU)=H2n+1(PU)=0 ...
Homotopy Groups
... times, and we take a subspace to be its boundary ∂(n) then the equivalence classes form a group, denoted πn(Y,y0), where y0 is in the image of the subspace ∂(n) ... We can define the action of one equivalence class on another, and so we get a group ... These groups are called the homotopy groups ...

Famous quotes containing the word groups:

    And seniors grow tomorrow
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    Philip Larkin (1922–1986)