Pullback of Bundles and Sections
If E is a vector bundle (or indeed any fiber bundle) over N and φ:M→N is a smooth map, then the pullback bundle φ*E is a vector bundle (or fiber bundle) over M whose fiber over x in M is given by (φ*E)x = Eφ(x).
In this situation, precomposition defines a pullback operation on sections of E: if s is a section of E over N, then the pullback section is a section of φ*E over M.
Read more about this topic: Pullback (differential Geometry)
Famous quotes containing the words bundles and/or sections:
“He bundles every forkful in its place,
And tags and numbers it for future reference,
So he can find and easily dislodge it
In the unloading. Silas does that well.
He takes it out in bunches like birds’ nests.”
—Robert Frost (1874–1963)
“For generations, a wide range of shooting in Northern Ireland has provided all sections of the population with a pastime which ... has occupied a great deal of leisure time. Unlike many other countries, the outstanding characteristic of the sport has been that it was not confined to any one class.”
—Northern Irish Tourist Board. quoted in New Statesman (London, Aug. 29, 1969)