Eine Verallgemeinerung Topologischer Mannigfaltigkeiten.
We exhibit a six dimensional manifold with a line bundle on it which is not the pullback of a bundle on .
We study secondary obstructions to representing a line bundle as the pull-back of a line bundle on and we interpret them geometrically.
A topological space X is called an -bubble (n is a natural number, is Čech cohomology with integer coefficients) if its n-dimensional cohomology is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any -bubbles; and (3) Every n-acyclic finite-dimensional -trivial metrizable compactum...