User's guide to equivariant methods in combinatorics. II.
Živaljević, Rade T. (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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Živaljević, Rade T. (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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Andrzej Weber (2004)
Open Mathematics
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We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).
Franz, Matthias (2006)
Documenta Mathematica
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Avner Ash, Glenn Stevens (1997)
Collectanea Mathematica
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Emili Bifet (1992)
Publicacions Matemàtiques
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We explain the philosophy behind the computations in [BDP] and place them in a wider conceptual setting. We also outline, for toric varieties, the resulting equivalent approach to some key results in that theory.
Cegarra, A.M., García-Calcines , J.M., Ortega, J.A. (2002)
Homology, Homotopy and Applications
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Hannu Honkasalo (1996)
Mathematica Scandinavica
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Jean-Luc Brylinski (1987)
Annales de l'institut Fourier
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In this article, we present two possible extensions of the classical theory of equivariant cohomology. The first, due to P. Baum, R. MacPherson and the author, is called the “delocalized theory". We attempt to present it in very concrete form for a circle action on a smooth manifold. The second is the cyclic homology of the crossed- product algebra of the algebra of smooth functions on a manifold, by the convolution algebra of smooth functions on a Lie group, when such Lie group act...
Raymond Stora (1997)
Recherche Coopérative sur Programme n°25
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Matthias Franz, Andrzej Weber (2005)
Annales de l’institut Fourier
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We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic -variety ( being a connected algebraic group) in terms of its equivariant cohomology provided that is pure. This is the case, for example, if is smooth and has only finitely many orbits. We work...