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J. Duflot 《Commentarii Mathematici Helvetici》1981,56(1):627-637
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We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a
new proof of the rigidity of the Witten genus, which exhibits a close relationship to recent work on non-equivariant orientations
of elliptic spectra.
Received: 24 May 2001; in final form: 4 October 2001 / Published online: 28 February 2002 相似文献
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Alejandro Adem 《Commentarii Mathematici Helvetici》1989,64(1):401-411
Partially supported by an NSF grant. 相似文献
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We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham complex of Malikov-Schechtman-Vaintrob of a manifold with a group action. The main idea in this paper is to synthesize the algebraic approach to classical equivariant cohomology due to H. Cartan,2 with the theory of differential vertex algebras, by using an appropriate notion of invariant theory. We also construct the vertex algebra analogues of the Mathai-Quillen isomorphism, the Weil and the Cartan models for equivariant cohomology, and the Chern-Weil map. We give interesting cohomology classes in the new theory that have no classical analogues. 相似文献
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Kathryn Hess 《Journal of Pure and Applied Algebra》2012,216(7):1680-1699
We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces of group actions. The importance of our enriched version of Moore’s theorem lies in its application to the construction of useful cochain algebra models for computing multiplicative structure in equivariant cohomology.In the special cases of homotopy orbits of circle actions on spaces and of group actions on simplicial sets, we obtain small, explicit cochain algebra models that we describe in detail. 相似文献
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J.P.C. Greenlees 《Journal of Pure and Applied Algebra》2019,223(7):2845-2871
The category of rational G-equivariant cohomology theories for a compact Lie group G is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of closed subgroups of G, with the topology corresponding to the topological poset of [7]. This is used to classify the collections of subgroups arising as the geometric isotropy of finite G-spectra. The ingredients for this classification are (i) the algebraic model of free spectra of the author and B. Shipley [14], (ii) the Localization Theorem of Borel–Hsiang–Quillen [21] and (iii) tom Dieck's calculation of the rational Burnside ring [4]. 相似文献
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We show that the well-known fact that the equivariant cohomology (with real coefficients) of a torus action is a torsion-free
module if and only if the map induced by the inclusion of the fixed point set is injective generalises to actions of arbitrary
compact connected Lie groups if one replaces the fixed point set by the set of points with isotropy rank equal to the rank
of the acting group. This is true essentially because the action on this set is always equivariantly formal. In case this
set is empty we show that the induced action on the set of points with highest occuring isotropy rank is Cohen-Macaulay. It
turns out that just as equivariant formality of an action is equivalent to equivariant formality of the action of a maximal
torus, the same holds true for equivariant injectivity and the Cohen-Macaulay property. In addition, we find a topological
criterion for equivariant injectivity in terms of orbit spaces. 相似文献
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We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field. 相似文献
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This paper presents a translation of a theorem of Cartan into an equivariant setting. This work is largely based on the study
of the homotopical algebra in the sense of Quillen of the category of simplicial objects over the category of rationalO
g-vector spaces. The application is a solution to the equivariant commutative cochain problem. This solution is slightly better
than the solution obtained earlier by Triantafillou in that the transformation groupG need not be finite. 相似文献
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We give a generalization of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action. We replace the manifold having a torus action by an equivariant map of manifolds having a compact connected Lie group action. This provides a systematic method for calculating the Gysin homomorphism in ordinary cohomology of an equivariant map. As an example, we recover a formula of Akyildiz-Carrell for the Gysin homomorphism of flag manifolds. 相似文献
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We construct the Chern character in the equivariant entire cyclic cohomology. We prove a general index theorem for theG-invariant Dirac operator.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065. 相似文献