Pontryagin Number

$k\_1,k\_2,...k\_m$ such that $k\_1+k\_2+...+k\_m=n$

$P\_\{k\_1,k\_2,...k\_m\}=p\_\{k\_1\}\backslash cup\; p\_\{k\_2\}\backslash cup\; ...\backslash cup\; p\_\{k\_m\}(M)$

Properties

1. Pontryagin numbers are oriented cobordism invariant; and together with Stiefel-Whitney numbers they determine an oriented manifold's oriented cobordism class.
2. Pontryagin numbers of closed Riemannian manifold (as well as Pontryagin classes) can be calculated as integrals of certain polynomial from curvature tensor of Riemannian manifold.
3. Such invariants as signature and $\backslash hat\; A$-genus can be expressed through Pontryagin numbers.

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