Hatcher 2.1.20

Hatcher, Algebraic Topology, Chapter 2, Section 1

20. Show that \widetilde{H}_n(X)\approx\widetilde{H}_{n+1}(SX) for all n, where SX is the suspension of X. More generally, thinking of SX as the union of two cones CX with their bases identified, compute the reduced homology groups of the union of any finite number of cones CX with their bases identified.
Proof.

\square

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