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There is a well-known in index theory "difference bundle" construction of Atiyah( see for example the original paper "Clifford modules"). And also there is a corresponding formula for the tensor ...

If $X$ is a compact smooth manifold, $K^{0}(X)$ can be defined as the algebraic $K_{0}$-group of $C^{\infty}(X)$. In order to do that we use the following equivalence relation: we say that two ...