Let be a complex, and let , be two cones whose polytopes intersect only in .

The complex is called "SUSPENSION" of K.

Define: by the equation -

.

Show that $\phi$ induces a homomorphism:

.

By the way, the homology groups here are the reduced ones... Which has no importance for p>0.

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What I've tried:

I thought I should define:

but what should I prove in order for it to be a homomorphism? it presereves the operation of chain-addition by definition of the cone operation...So what is left to do? can someone help me?

]

Thanks in advance