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Displaying similar documents to “Descriptions of Čech cohomology”

Pairings, duality, amenability and bounded cohomology

Jacek Brodzki, Graham A. Niblo, Nick J. Wright (2012)

Journal of the European Mathematical Society

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We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.

Double complexes and vanishing of Novikov cohomology

Hüttemann, Thomas (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15. We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new...

Cutting description of trivial 1-cohomology

Andrzej Czarnecki (2014)

Annales Polonici Mathematici

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

Compactly supported cohomology of systolic 3-pseudomanifolds

Roger Gómez-Ortells (2014)

Colloquium Mathematicae

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We show that the second group of cohomology with compact supports is nontrivial for three-dimensional systolic pseudomanifolds. It follows that groups acting geometrically on such spaces are not Poincaré duality groups.