Cohomology theories on compact and locally compact spaces.

Edwin Spanier

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

A note on the general cohomology theory

Wu, Ta-Sun (1959)

Portugaliae mathematica

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On ${\overset{ˇ}{H}}^{n}$ -bubbles in n-dimensional compacta

Umed Karimov, Dušan Repovš (1998)

Colloquium Mathematicae

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

The cohomology ring of polygon spaces

Jean-Claude Hausmann, Allen Knutson (1998)

Annales de l'institut Fourier

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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...