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Line bundles with c 1 L 2 = 0 . A six dimensional example

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We exhibit a six dimensional manifold with a line bundle on it which is not the pullback of a bundle on S 2 .

Line bundles with c 1 L 2 = 0 . Higher order obstruction

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study secondary obstructions to representing a line bundle as the pull-back of a line bundle on S 2 and we interpret them geometrically.

On H ˇ n -bubbles in n-dimensional compacta

Umed Karimov, Dušan Repovš (1998)

Colloquium Mathematicae

A topological space X is called an H ˇ n -bubble (n is a natural number, H ˇ n is Čech cohomology with integer coefficients) if its n-dimensional cohomology H ˇ n ( X ) is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable H ˇ n -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any H ˇ 2 -bubbles; and (3) Every n-acyclic finite-dimensional L H ˇ n -trivial metrizable compactum...

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