Displaying similar documents to “Cohomology theories on compact and locally compact spaces.”

On H ˇ n -bubbles in n-dimensional compacta

Umed Karimov, Dušan Repovš (1998)

Colloquium Mathematicae

Similarity:

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...

The cohomology ring of polygon spaces

Jean-Claude Hausmann, Allen Knutson (1998)

Annales de l'institut Fourier

Similarity:

We compute the integer cohomology rings of the “polygon spaces”introduced in [F. Kirwan, Cohomology rings of moduli spaces of vector bundles over Riemann surfaces, J. Amer. Math. Soc., 5 (1992), 853-906] and [M. Kapovich & J. Millson, the symplectic geometry of polygons in Euclidean space, J. of Diff. Geometry, 44 (1996), 479-513]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we calculate its kernel using ideas from...