Conormality at the zero section

Next we turn to the case of a real vector bundle W −→ Y over a compact manifold Y and define the space of conormal distributions on the total space W of the vector bundle with respect to (i.e. only singular at) the zero section 0W . The latter is a compact embedded submanifold canonically isomorphic to Y. Before I do this, I want to point out some further properties in the case of the conormal distributions with respect to the origin of a vector space. In particular there is another important invariance property, the proof of which I want to go through. I will also indicate in a simple example how these spaces can be used. First, these distibutions can be integrated