Construction of The Thom Space
One way to construct this space is as follows. Let
- p : E → B
be a rank k real vector bundle over the paracompact space B. Then for each point b in B, the fiber Fb is a k-dimensional real vector space. We can form an associated sphere bundle Sph(E) → B by taking the one-point compactification of each fiber separately. Finally, from the total space Sph(E) we obtain the Thom complex T(E) by identifying all the new points to a single point, which we take as the basepoint of T(E).
Read more about this topic: Thom Space
Famous quotes containing the words construction of the, construction of, construction and/or space:
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (1729–1797)
“No construction stiff working overtime takes more stress and straining than we did just to stay high.”
—Gus Van Sant, U.S. screenwriter and director, and Dan Yost. Bob Hughes (Matt Dillon)
“The limitless future of childhood shrinks to realistic proportions, to one of limited chances and goals; but, by the same token, the mastery of time and space and the conquest of helplessness afford a hitherto unknown promise of self- realization. This is the human condition of adolescence.”
—Peter Blos (20th century)