Stable Normal Bundle - Construction Via Classifying Spaces

Construction Via Classifying Spaces

An n-manifold M has a tangent bundle, which has a classifying map (up to homotopy)

Composing with the inclusion yields (the homotopy class of a classifying map of) the stable tangent bundle. The normal bundle of an embedding ( large) is an inverse for, such that the Whitney sum \tau_M\oplus \nu_M \colon M \to BO(n+k) is trivial. The homotopy class of the composite is independent of the choice of inverse, classifying the stable normal bundle .

Read more about this topic:  Stable Normal Bundle

Famous quotes containing the words construction and/or spaces:

    “There’s no art
    To find the mind’s construction in the face:
    He was a gentleman on whom I built
    An absolute trust.”
    —William Shakespeare (1564–1616)

    “Surely, we are provided with senses as well fitted to penetrate the spaces of the real, the substantial, the eternal, as these outward are to penetrate the material universe. Veias, Menu, Zoroaster, Socrates, Christ, Shakespeare, Swedenborg,—these are some of our astronomers.”
    —Henry David Thoreau (1817–1862)