# Tag Info

## Hot answers tagged grassmannians

Accepted

### When can one continuously prescribe a unit vector orthogonal to a given orthonormal system?

$\def\RR{\mathbb{R}}$ This problem was solved by Whitehead, G. W., Note on cross-sections in Stiefel manifolds, Comment. Math. Helv. 37, 239-240 (1963). ZBL0118.18702. Such sections exist only in ...
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### When can one continuously prescribe a unit vector orthogonal to a given orthonormal system?

Unless I'm missing something, I think that the hairy ball theorem states precisely that you cannot do this when $n = 3$ and $k = 1$. I'm not sure what happens for other values of $n$ and $k$.
• 15k

Accepted

### Steenrod operations on cohomology of grassmannians

As in Prasit's comment, the action of the Steenrod squares on the Stiefel-Whitney classes of any vector bundle are given by Wu's formula  Sq^i(w_j) = \sum_{t=0}^i \binom{j+t-i-1}{t} w_{i-t} w_{j+t}. ...
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