Hopf cohomology vanishing via approximation by Hochschild cohomology
Akira Masuoka (2003)
Banach Center Publications
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Akira Masuoka (2003)
Banach Center Publications
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G. I. Sharygin (2003)
Banach Center Publications
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We employ the notion of the universal differential calculus to propose yet another approach to the Hopf-type cohomology of Hopf algebras.
John W. Rutter (1976)
Colloquium Mathematicae
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Pierre Berthelot (2012)
Rendiconti del Seminario Matematico della Università di Padova
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Malakhaltsev, M.A. (1999)
Lobachevskii Journal of Mathematics
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Wilhelm Singhof (1978)
Mathematische Zeitschrift
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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.
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...
Takeo Ohsawa (1992)
Mathematische Zeitschrift
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Kermit Sigmon (1975)
Aequationes mathematicae
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P.J. HUBER (1961)
Mathematische Annalen
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Urs Würgler (1979)
Manuscripta mathematica
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P. Berthelot, A. Ogus (1983)
Inventiones mathematicae
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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.
W. Kucharz (2005)
Annales Polonici Mathematici
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A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.
James P. Lin (1980)
Commentarii mathematici Helvetici
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Hisashi Kasuya (2016)
Complex Manifolds
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For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ, C) of the solvmanifold Γ. In this note, we give a quick introduction to the construction of such A*Γ including a simple proof of H*(A*Γ) ≅ H*(Γ, C).