High Quality Content by WIKIPEDIA articles! In mathematics, the Thom space or Thom complex (named after Rene Thom) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact 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 infty, which we take as the basepoint of T(E).

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