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Cutting description of trivial 1-cohomology

Andrzej Czarnecki (2014)

Annales Polonici Mathematici

A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.

Maximal equicontinuous factors and cohomology for tiling spaces

Marcy Barge, Johannes Kellendonk, Scott Schmieding (2012)

Fundamenta Mathematicae

We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that in degree one this map is injective and has torsion free cokernel. We show by example, however, that, in degree one, the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology.

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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