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:
“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)
“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)
“The construction of life is at present in the power of facts far more than convictions.”
—Walter Benjamin (1892–1940)
“When Paul Bunyan’s loggers roofed an Oregon bunkhouse with shakes, fog was so thick that they shingled forty feet into space before discovering they had passed the last rafter.”
—State of Oregon, U.S. public relief program (1935-1943)