共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Generalized Dirichlet to Neumann operator on invariant differential forms and equivariant cohomology
Qusay S.A. Al-Zamil James Montaldi 《Topology and its Applications》2012,159(3):823-832
In recent work, Belishev and Sharafutdinov show that the generalized Dirichlet to Neumann (DN) operator Λ on a compact Riemannian manifold M with boundary ∂M determines de Rham cohomology groups of M. In this paper, we suppose G is a torus acting by isometries on M. Given X in the Lie algebra of G and the corresponding vector field XM on M, Witten defines an inhomogeneous coboundary operator dXM=d+ιXM on invariant forms on M. The main purpose is to adapt Belishev-Sharafutdinov?s boundary data to invariant forms in terms of the operator dXM in order to investigate to what extent the equivariant topology of a manifold is determined by the corresponding variant of the DN map. We define an operator ΛXM on invariant forms on the boundary which we call the XM-DN map and using this we recover the XM-cohomology groups from the generalized boundary data (∂M,ΛXM). This shows that for a Zariski-open subset of the Lie algebra, ΛXM determines the free part of the relative and absolute equivariant cohomology groups of M. In addition, we partially determine the ring structure of XM-cohomology groups from ΛXM. These results explain to what extent the equivariant topology of the manifold in question is determined by ΛXM. 相似文献
3.
The recursive nature of cominuscule Schubert calculus 总被引:1,自引:0,他引:1
The necessary and sufficient Horn inequalities which determine the non-vanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson coefficients on smaller Grassmannians. We show how non-vanishing in the Schubert calculus for cominuscule flag varieties is similarly recursive. For these varieties, the non-vanishing of products of Schubert classes is controlled by the non-vanishing products on smaller cominuscule flag varieties. In particular, we show that the lists of Schubert classes whose product is non-zero naturally correspond to the integer points in the feasibility polytope, which is defined by inequalities coming from non-vanishing products of Schubert classes on smaller cominuscule flag varieties. While the Grassmannian is cominuscule, our necessary and sufficient inequalities are different than the classical Horn inequalities. 相似文献
4.
Kiyoshi Igusa 《Topology》2004,43(6):1469-1510
We use the duality between compactly supported cohomology of the associative graph complex and the cohomology of the mapping class group to show that the duals of the Kontsevich cycles [Wλ] correspond to polynomials in the Miller-Morita-Mumford classes. We also compute the coefficients of the first two terms of this polynomial. This extends the results of (Combinatorial Miller-Morita-Mumford classes and Witten cycles, math.GT/0207042, 2002), giving a more detailed answer to a question of Kontsevich (Commun. Math. Phys. 147(1) (1992) 1) and verifying more of the conjectured formulas of Arbarello and Cornalba (J. Algebraic Geom. 5 (1996) 705). 相似文献
5.
Diane E. Davis 《Journal of Pure and Applied Algebra》2011,215(5):902-926
This paper is the second in a series leading to a type Bn geometric Littlewood-Richardson rule. The rule will give an interpretation of the Bn Littlewood-Richardson numbers as an intersection of two odd-orthogonal Schubert varieties and will consider a sequence of linear and quadratic deformations of the intersection into a union of odd-orthogonal Schubert varieties. This paper describes the setup for the rule and specifically addresses results for quadratic deformations, including a proof that at each quadratic degeneration, the results occur with multiplicity one. This work is strongly influenced by Vakil’s [14]. 相似文献
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7.
Liviu I. Nicolaescu 《Advances in Mathematics》2010,224(6):2361-2434
With an eye towards index theoretic applications we describe a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in Cn⊕Cn. This is a natural compactification of the space of hermitian n×n matrices. The closures of the strata define integral cycles, and we investigate their intersection theoretic properties. We achieve this by blending Morse theoretic ideas, with techniques from o-minimal (or tame) geometry and geometric integration theory. 相似文献
8.
Goutam Mukherjee 《Topology and its Applications》2010,157(6):1015-1032
We introduce equivariant twisted cohomology of a simplicial set equipped with simplicial action of a discrete group and prove that for suitable twisting function induced from a given equivariant local coefficients, the simplicial version of Bredon-Illman cohomology with local coefficients is isomorphic to equivariant twisted cohomology. The main aim of this paper is to prove a classification theorem for equivariant simplicial cohomology with local coefficients. 相似文献
9.
Bernhard Hanke 《Mathematische Annalen》2005,332(3):677-696
By results of Löffler and Comezaña, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G=S1××S1, we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of Sinha [22]. This is used in order to determine the image of the Pontrjagin-Thom map for toralG. 相似文献
10.
William Kronholm 《Topology and its Applications》2012,159(5):1380-1387
In this paper, we compute the RO(Z/2)-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions. 相似文献
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12.
Haibao Duan 《Advances in Mathematics》2003,180(1):112-133
We study integration along Bott-Samelson cycles. As an application the degree of a Schubert variety on a flag manifold G/B is evaluated in terms of certain Cartan numbers of G. 相似文献
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14.
Markus Szymik 《Topology and its Applications》2007,154(11):2323-2332
Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner [S. Waner, Equivariant RO(G)-graded bordism theories, Topology and its Applications 17 (1984) 1-26], the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterised in terms of congruences. This is first shown to be a stable problem, and then solved using methods of equivariant stable homotopy theory with respect to a semi-free G-universe. 相似文献
15.
In their recent preprint, Baldwin, Ozsváth and Szabó defined a twisted version (with coefficients in a Novikov ring) of a spectral sequence, previously defined by Ozsváth and Szabó, from Khovanov homology to Heegaard–Floer homology of the branched double cover along a link. In their preprint, they give a combinatorial interpretation of the E3-term of their spectral sequence. The main purpose of the present paper is to prove directly that this E3-term is a link invariant. We also give some concrete examples of computation of the invariant. 相似文献
16.
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
17.
Lisbeth Fajstrup 《manuscripta mathematica》1996,91(1):211-221
Summary We study a generalized equivariantK-theory introduced by M. Karoubi. We prove, that it is anRO (G, U)-graded cohomology-theory and that the associated Tate spectrum is rational whenG is finite. This implies that for finite groups, the Atiyah-Segal Real equivariantK-theories have rational Tate theory.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag 相似文献
18.
Linda Chen 《Advances in Mathematics》2003,174(1):1-34
We study two aspects of quantum Schubert calculus: a presentation of the (small) quantum cohomology ring of partial flag manifolds and a quantum Giambelli formula. Our proof gives a relationship between universal Schubert polynomials as defined by Fulton and quantum Schubert polynomials, as defined by Fomin, Gelfand, and Postnikov, and later extended by Ciocan-Fontanine. Intersection theory on hyperquot schemes is an essential element of the proof. 相似文献
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Mohammad Obiedat 《Topology and its Applications》2006,153(12):2182-2189
The equivariant real, complex and quaternionic vector fields on spheres problem is reduced to a question about the equivariant J-groups of the projective spaces. As an application of this reduction, we give a generalization of the results of Namboodiri [U. Namboodiri, Equivariant vector fields on spheres, Trans. Amer. Math. Soc. 278 (2) (1983) 431-460], on equivariant real vector fields, and Önder [T. Önder, Equivariant cross sections of complex Stiefel manifolds, Topology Appl. 109 (2001) 107-125], on equivariant complex vector fields, which avoids the restriction that the representation containing the sphere has enough orbit types. 相似文献