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Topic: Same Homology but Not Homotopic.
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S4M

Posts: 28
From: NYC
Registered: 12/8/12
Same Homology but Not Homotopic.
Posted: Dec 10, 2012 2:51 AM
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Hi, All:

If spaces X,Y are homotopically-equivalent, then their
homology groups and fundamental groups are the same.

I know the converse is not true, i.e., if X,Y have the same homology, they are not necessarily homotopically equivalent. But I don't know any examples. I imagine something like Eilenberg-MacLane spaces; maybe some Abelianization issues may be used.

Anyone know of an example?

Thanks.



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