Re: induced homomorphism on homology groups

In <1141278781.681563.69770@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
03/01/2006
at 09:53 PM, berthuffman@xxxxxxxxx said:

for a continuous map f : X --> Y we can an induced map on the free
abelian groups spanned by singular n-chains for each n, f_# : C_n
(X) --> C_n (Y), where we simply compose an n-chain with f.

Not quite. You compose each of the symplexes in the n-chain with f.

Now is this map simply defined by f_* ( [s] ) = [ f o s ], where s
is an n-chain in X and [s] is the equivalence class of s?

No, it's defined by f_* ( [s] ) = [ f_#(s) ]

so how does that subset condition imply induced homomorphism?

Because f_# satisfies the conditions of the theorem, which you stated
you had verified.

if that wasn't satisfied there wouldn't be an induced homomorphism?

The theorem states that it *is* satisfied.

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Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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