Displaying similar documents to “André-Quillen cohomology for commutative coalgebras”

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.

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.

Spectral sequences for commutative Lie algebras

Friedrich Wagemann (2020)

Communications in Mathematics

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We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2 . In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley-Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.

Nash cohomology of smooth manifolds

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.