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Let $X \subset Y$ be two smooth manifolds. To the inclusion $I:X \to Y$ corresponds the so called wrong-way map in $K-theory$ $i_!:K(X) \to K(Y)$. It is constructed as follows: to the inclusion $X \...

I apologize for the vague title. Let $M$ be a compact smooth manifold, then we have $T^*M$ and hence $\wedge^pT^*M$ as vector bundles on $M$. There for we have $$ \sum (-1)^p[\wedge^pT^*M] \in K(M). $...