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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.

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Novikov's conjecture for higher signatures in case $\pi(M) = \mathbb{Z}^k$

I'm interested whether there is a simple proof for Novikov's conjecture for higher signatures in case of fundamental group $\pi(M) = \mathbb{Z}^k$. I guess that something can be found in Kasparov's wo …