Conversely, general bundle maps can be reduced to bundle maps over a fixed base space using the notion of a pullback bundle.
2.
Conversely, general bundle maps can be reduced to bundle maps over a fixed base space using the notion of a pullback bundle.
3.
This leads, for example, to the notion of a "'smooth bundle map "'between smooth fiber bundles over a smooth manifold.
4.
Vector bundle morphisms are a special case of the notion of a bundle map between fiber bundles, and are also often called "'( vector ) bundle homomorphisms " '.
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Mappings between total spaces of fiber bundles that " commute " with the projection maps are known as bundle maps, and the class of fiber bundles forms a section of " E ".
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Outside the hyperelliptic cases, Noether proved that ( in modern language ) the canonical bundle is normally generated : the symmetric powers of the space of sections of the canonical bundle map onto the sections of its tensor powers.
7.
A degree one normal map ( f, b ) \ colon M \ to X consists of the following data : an n-dimensional oriented closed manifold M, a map f which is of degree one ( that means f _ * ( [ M ] ) = [ X ], and a bundle map b \ colon TM \ oplus \ varepsilon ^ k \ to \ xi from the stable tangent bundle of M to some bundle \ xi over X.
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