### 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

... 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

... 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(

... In particular, using the isomorphism between the

*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

From the juniors today,

And even swimming *groups* can fade,

Games mistresses turn grey.”

—Philip Larkin (1922–1986)