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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


Hi, All:
If spaces X,Y are homotopicallyequivalent, 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 EilenbergMacLane spaces; maybe some Abelianization issues may be used.
Anyone know of an example?
Thanks.



