suspension isomorphism

Proposition 1.

Let X be a topological spaceMathworldPlanetmath. There is a natural isomorphism


where SX stands for the unreduced suspension of X.

If X has a basepoint, there is a natural isomorphism


where ΣX is the reduced suspension.

A similar propositionPlanetmathPlanetmathPlanetmath holds with homologyMathworldPlanetmathPlanetmath replaced by cohomology.

In fact, these propositions follow from the Eilenberg-Steenrod axioms without the dimension axiom, so they hold for any generalized (co)homology theory in place of integral (co)homology.

Title suspension isomorphism
Canonical name SuspensionIsomorphism
Date of creation 2013-03-22 13:25:58
Last modified on 2013-03-22 13:25:58
Owner antonio (1116)
Last modified by antonio (1116)
Numerical id 4
Author antonio (1116)
Entry type Theorem
Classification msc 55N99
Related topic Suspension