Twisted K-theory and obstructions against positive scalar curvature metrics

We decompose the twisted index obstruction $θ(M)$ against positive scalar curvature metrics for oriented manifolds with spin universal cover into a pairing of a twisted $K$-homology with a twisted $K$-theory class and prove that $θ(M)$ does not vanish if $M$ is an orientable enlargeable manifold with spin universal cover.

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