Stable Normal Bundle
Abstract manifolds have a canonical tangent bundle, but do not have a normal bundle: only an embedding (or immersion) of a manifold in another yields a normal bundle. However, since every compact manifold can be embedded in, by the Whitney embedding theorem, every manifold admits a normal bundle, given such an embedding.
There is in general no natural choice of embedding, but for a given M, any two embeddings in for sufficiently large N are regular homotopic, and hence induce the same normal bundle. The resulting class of normal bundles (it is a class of bundles and not a specific bundle because N could vary) is called the stable normal bundle.
Read more about this topic: Normal Bundle
Famous quotes containing the words stable, normal and/or bundle:
“This stable is a Prince’s court.
This crib His chair of state;
The beasts are parcel of His pomp,
The wooden dish His plate.”
—Robert Southwell (1561?–1595)
“You have promise, Mlle. Dubois, but you must choose between an operatic career and what is usually called “a normal life.” Though why it is so called is beyond me.”
—Eric Taylor, Leroux, and Arthur Lubin. M. Villeneuve (Frank Puglia)
“We styled ourselves the Knights of the Umbrella and the Bundle; for, wherever we went ... the umbrella and the bundle went with us; for we wished to be ready to digress at any moment. We made it our home nowhere in particular, but everywhere where our umbrella and bundle were.”
—Henry David Thoreau (1817–1862)