The companion concept to associated bundles is the reduction of the structure group of a -bundle . We ask whether there is an -bundle, such that the associated -bundle is, up to isomorphism. More concretely, this asks whether the transition data for can consistently be written with values in . In other words, we ask to identify the image of the associated bundle mapping (which is actually a functor).
Read more about this topic: Associated Bundle
Famous quotes containing the words reduction of, reduction, structure and/or group:
“The reduction of nuclear arsenals and the removal of the threat of worldwide nuclear destruction is a measure, in my judgment, of the power and strength of a great nation.”
—Jimmy Carter (James Earl Carter, Jr.)
“The reduction of nuclear arsenals and the removal of the threat of worldwide nuclear destruction is a measure, in my judgment, of the power and strength of a great nation.”
—Jimmy Carter (James Earl Carter, Jr.)
“Vashtar: So it’s finished. A structure to house one man and the greatest treasure of all time.
Senta: And a structure that will last for all time.
Vashtar: Only history will tell that.
Senta: Sire, will he not be remembered?
Vashtar: Yes, he’ll be remembered. The pyramid’ll keep his memory alive. In that he built better than he knew.”
—William Faulkner (1897–1962)
“For me, as a beginning novelist, all other living writers form a control group for whom the world is a placebo.”
—Nicholson Baker (b. 1957)