The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection
of Stiefel-Whitney classes such that their
cup product has the same dimension as the manifold ,
this cup product can be evaluated on the manifold 's
fundamental class . The resulting number is called
the Pontryagin number for that combination of
Pontryagin classes.

The most important aspect of Stiefel-Whitney numbers is that they are bordism invariant. Together, Pontryagin and Stiefel-Whitney
numbers determine an oriented manifold 's bordism
class.

See also Chern Number ,

Pontryagin
Number ,

Stiefel-Whitney Class
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Stiefel-Whitney Number."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Stiefel-WhitneyNumber.html

Subject classifications