### K-homology class of the Euler characteristic operator

When studying the Atiyah-Singer index theorem one usually sees four main examples. Atiyah-Singer operator: Its topological index is the \(\hat{A}\)-genus and its analytical index can be related to scalar curvature. This shows that the \(\hat{A}\)-genus of a manifold is an obstruction to the existence of a Riemannian metric of positive scalar curvature on it. Signature … Continue reading "K-homology class of the Euler characteristic operator"

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