Curvature operators and rational cobordism
Abstract
We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted A genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.
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