= Coorientation
= Transverse orientation
{synonym}
For a codimension-one tangent distribution, a <coorientation> is an orientation of its normal quotient line bundle. An oriented real line bundle is trivial: local positive sections can be combined with a partition of unity without cancellation. Hence a cooriented distribution is the kernel of a global nowhere-vanishing <one-form>. This choice is independent of the orientation of the ambient manifold, and reversing it does not change the <Godbillon-Vey invariant>.
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