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- Jun 20, 2014

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Let $f : M \to M$ be a self-map of a smooth manifold $M$. Prove that the graph of $f$ is transversal to the diagonal of $M$ if and only if the fixed points of $M$ are nondegenerate, i.e., for all fixed points $p$, $+1$ is not an eigenvalue of $df_p$.

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