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:
“And neigh like Boanerges—
Then—punctual as a Star
Stop—docile and omnipotent
At its own stable door—”
—Emily Dickinson (1830–1886)
“Love brings to light the lofty and hidden characteristics of the lover—what is rare and exceptional in him: to that extent it can easily be deceptive with respect to what is normal in him.”
—Friedrich Nietzsche (1844–1900)
“In the quilts I had found good objects—hospitable, warm, with soft edges yet resistant, with boundaries yet suggesting a continuous safe expanse, a field that could be bundled, a bundle that could be unfurled, portable equipment, light, washable, long-lasting, colorful, versatile, functional and ornamental, private and universal, mine and thine.”
—Radka Donnell-Vogt, U.S. quiltmaker. As quoted in Lives and Works, by Lynn F. Miller and Sally S. Swenson (1981)