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:

    “No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
    —T.S. (Thomas Stearns)

    “Deep down, the US, with its space, its technological refinement, its bluff good conscience, even in those spaces which it opens up for simulation, is the only remaining primitive society.”
    —Jean Baudrillard (b. 1929)