Algebraic Topology · Problem 25

The Fundamental Group — Allen Hatcher

Mathematics — Topology · suspension

Problem

X

is a CW complex with components

X_\alpha

, show that the suspension

SX

is homotopy equivalent to

Y \vee_\alpha SX_\alpha

for some graph

Y

. In the case that

X

is a finite graph, show that

SX

is homotopy equivalent to a wedge sum of circles and 2-spheres.