Hatcher-Algebraic-Topology · Problem 4.J.1

Homotopy Theory

Mathematics — Graph Theory · loopspace-of-a-suspension

Problem

Show that ΩΣX\Omega\Sigma X for a nonconnected CW complex XX reduces to the connected case by showing that each path-component of ΩΣX\Omega\Sigma X is homotopy equivalent to ΩΣ⋁αXα\Omega\Sigma\bigvee_\alpha X_\alpha where the XαX_\alpha's are the components of XX.

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