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I am curious to find examples of maps f:X-->X ; X an n-dimensional manifold

that induce isomorphisms on , say, the first k<n homology groups, but not

so on the remaining n-k groups. I can see if we had maps g:X-->Y, we could start

with Y=X, let f be an automorphism, and then cap some boundaries of X, i.e., all j-

boundaries for j>k , but not so for maps f:X-->X . Any Ideas?

Thanks.

others, so that the induced maps on H_k(X) are not isomorphsims

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# Induced Maps on Homology

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