... allowing the fiberover each point in the manifold to be the actualplane represented by that point. If one consid-ers the manifold as the collection of names of the planes, then the bundle is the ... leftmost 1 on the tape, and the machine is set to the initial state q0. The output of the function (if any) is the numberof 1s on the tape when the machine halts, afterexecuting the program, ... equivalent to the pullbackg∗(E)−→B, then the class assigned toE−→B istheimageoftheclassassignedtoE−→Bunder the map g∗:H∗(B)−→H∗(B).When the cohomology of the base space...