Pontryagin class

In mathematics, the Pontryagin classes are certain characteristic classes. The Pontryagin class lies in cohomology groups with index a multiple of four. It applies to real vector bundles.

Pontryagin classes of a manifold

The Pontryagin classes of a smooth manifold are defined to be the Pontryagin classes of its tangent bundle.

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Novikov's theorem states that if manifolds are homeomorphic then their rational Pontryagin classes

Related Topics:
Novikov's theorem - Homeomorphic

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:p_k(M,mathbb{Q}) in H^{4k}(M,mathbb{Q})

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are the same.

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If the dimension is at least five, there at most finitely many different smooth manifolds with given homotopy type and Pontryagin classes.

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