Construction
In general it is enough to explain the transition from a bundle with fiber, on which acts, to the associated principal bundle (namely the bundle where the fiber is, considered to act by translation on itself). For then we can go from to, via the principal bundle. Details in terms of data for an open covering are given as a case of descent.
This section is organized as follows. We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle. This then specializes to the case when the specified fibre is a principal homogeneous space for the left action of the group on itself, yielding the associated principal bundle. If, in addition, a right action is given on the fibre of the principal bundle, we describe how to construct any associated bundle by means of a fibre product construction.
Read more about this topic: Associated Bundle
Famous quotes containing the word construction:
“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 authors personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)
“Theres no art
To find the minds construction in the face.”
—William Shakespeare (15641616)
“The construction of life is at present in the power of facts far more than convictions.”
—Walter Benjamin (18921940)