# 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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