Duality and distribution cohomology of manifolds
C. Denson Hill, M. Nacinovich (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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C. Denson Hill, M. Nacinovich (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Martintxo Saralegi-Aranguren, Robert Wolak (2006)
Annales Polonici Mathematici
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We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group...
Vladimir Gol'dshtein, Marc Troyanov (1998)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Christopher Deninger (1987)
Mathematische Annalen
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W. Jakobsche (1991)
Fundamenta Mathematicae
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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.
Pierre Berthelot (2012)
Rendiconti del Seminario Matematico della Università di Padova
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Mariusz Wodzicki (1991)
Inventiones mathematicae
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M. Herrera, D. Liebermann (1971)
Inventiones mathematicae
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José Ignacio Royo Prieto, Martintxo Saralegi-Aranguren, Robert Wolak (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does...
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.
Stephen A. Selesnick (1973)
Mathematische Zeitschrift
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John W. Rutter (1976)
Colloquium Mathematicae
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