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)
“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’s no art
To find the mind’s construction in the face:
He was a gentleman on whom I built
An absolute trust.”
—William Shakespeare (1564–1616)
“The secret ones around a stone
Their lips withdrawn in meet surprise
Lie still, being naught but bone
With naught but space within their eyes....”
—Allen Tate (1899–1979)