Freudenthal suspension theorem

The Freudenthal'sche Einhängungssatz is a set from the mathematical branch of algebraic topology, it forms a basis for the stable homotopy theory.

The statement is the following:

Be and a -connected CW - complex. Then the induced by the device to attach picture

For an isomorphism and surjective.

For the stable homotopy groups it follows that

Is an isomorphism and surjective.

Generalization: Be and a -connected CW - complex. Be a finite CW - complex for. Then

For all a bijection between the sets of homotopy classes.