共查询到20条相似文献,搜索用时 46 毫秒
1.
Laura Scull 《Transactions of the American Mathematical Society》2008,360(5):2505-2525
In the equivariant category of spaces with an action of a finite group, algebraic `minimal models' exist which describe the rational homotopy for -spaces which are 1-connected and of finite type. These models are diagrams of commutative differential graded algebras. In this paper we prove that a model category structure exists on this diagram category in such a way that the equivariant minimal models are cofibrant objects. We show that with this model structure, there is a Quillen equivalence between the equivariant category of rational -spaces satisfying the above conditions and the algebraic category of the models.
2.
For an algebra
with an action of a Hopf algebra
we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for
. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space
for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating
equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces. 相似文献
3.
Hui Li 《Transactions of the American Mathematical Society》2003,355(11):4543-4568
Assume is a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case . We give a complete list of the possible manifolds, and determine their equivariant cohomology rings and equivariant Chern classes. Some of these manifolds are classified up to diffeomorphism. We also show the existence for a few cases.
4.
5.
We define an equivariant K
0-theory for Yetter–Drinfeld algebras over a Hopf algebra with an invertible antipode. We then show that this definition can be generalized to all Hopf-module algebras. We show that there exists a pairing, generalizing Connes pairing, between this theory and a suitably defined Hopf algebra equivariant cyclic cohomology theory. 相似文献
6.
Sergei M. Ageev Dusan Repovs 《Proceedings of the American Mathematical Society》2002,130(5):1539-1550
Ancel's method of fiberwise trivial relations is applied to the problem of characterization of absolute equivariant extensors. We obtain a generalization of Jaworowski's theorem on characterization of equivariant extensors lying in to the case when the space is infinite-dimensional, has infinitely many orbit types and the acting compact group is not necessarily a Lie group.
7.
In this paper a closing lemma for nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small equivariant perturbation.
8.
Adam Korá nyi Ró bert Szoke 《Proceedings of the American Mathematical Society》2006,134(12):3449-3456
We prove an equivariant analogue of Chevalley's isomorphism theorem for polynomial, or maps.
9.
We give a detailed proof of the rigidity theorem for elliptic genera. Using the Lefschetz fixed point formula we carefully analyze the relation between the characteristic power series defining the elliptic genera and the equivariant elliptic genera. We show that equivariant elliptic genera converge to Jacobi functions which are holomorphic. This implies the rigidity of elliptic genera. Our approach can be easily modified to give a proof of the rigidity theorem for the elliptic genera of level .
10.
For a finite group G we define an involution on the equivariant Whitehead group given by reversing the direction of an equivariant h-cobordism. It turns out that the involution is not compatible with the splitting of the equivariant Whitehead group into a direct sum of algebraic Whitehead groups, certain correction terms involving the transfer maps of the normal sphere bundles of the various fixed point sets come in. However, if the group has odd order, these transfer maps all vanish. We prove a duality formula for a G-homotopy equivalence (f f): (M; M) (N, N) relating the equivariant Whitehead torsion of f and (f,f). 相似文献
11.
Paul Baum Hervé Oyono-Oyono Thomas Schick Michael Walter 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2010,80(2):149-173
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups $K^{G}_{*}(X)$ , using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the “official” equivariant K-homology groups) and show that these are isomorphisms. 相似文献
12.
The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal G-bundles, including those over manifolds, those over orbifolds, as well as equivariant principal G-bundles. In this paper, we study differential geometry of these objects, including connections and holonomy maps. We also
introduce a Chern–Weil map for these principal bundles and prove that the characteristic classes obtained coincide with the
universal characteristic classes. As an application, we recover the equivariant Chern–Weil map of Bott–Tu. We also obtain
an explicit chain map between the Weil model and the simplicial model of equivariant cohomology which reduces to the Bott–Shulman
map when the manifold is a point.
P. Xu Research partially supported by NSF grant DMS-03-06665. 相似文献
13.
Dev Sinha 《Proceedings of the American Mathematical Society》2002,130(1):271-281
In this paper we compute homotopical equivariant bordism for the group , namely , geometric equivariant bordism , and their quotient as modules over geometric bordism. This quotient is a module of stable transversality obstructions. We construct these rings from knowledge of their localizations.
14.
Georgios Pappas 《Compositio Mathematica》2000,121(1):79-104
We describe a general method for calculating equivariant Euler characteristics. The method exploits the fact that the -filtration on the Grothendieck group of vector bundles on a Noetherian quasi-projective scheme has finite length; it allows us to capture torsion information which is usually ignored by equivariant Riemann–Roch theorems. As applications, we study the G-module structure of the coherent cohomology of schemes with a free action by a finite group G and, under certain assumptions, we give an explicit formula for the equivariant Euler characteristic
in the Grothendieck group of finitely generated Z[G]-modules, when X is a curve over Z and G has prime order. 相似文献
15.
We prove an equivariant Riemann–Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known
case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in . We then prove and shed some further light on a divisibility result that yields a formula with integral coefficients. Moreover,
we give variants of the main theorem for equivariant locally free sheaves of higher rank. 相似文献
16.
Steven Lillywhite 《Transactions of the American Mathematical Society》2003,355(7):2771-2793
We define and discuss -formality for certain spaces endowed with an action by a compact Lie group. This concept is essentially formality of the Borel construction of the space in a category of commutative differential graded algebras over . These results may be applied in computing the equivariant cohomology of their loop spaces.
17.
Pedro F. dos Santos Paulo Lima-Filho 《Transactions of the American Mathematical Society》2004,356(12):4701-4736
In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group . Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour's quaternionic -theory, and the other one classifies an equivariant cohomology theory which is a natural recipient of characteristic classes for quaternionic bundles over Real spaces .
18.
We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex G-variety X by its associated arc space J ∞ X, with its induced G-action. This not only allows us to obtain geometric classes in equivariant cohomology of arbitrarily high degree, but also provides more flexibility for equivariantly deforming classes and geometrically interpreting multiplication in the equivariant cohomology ring. Under appropriate hypotheses, we obtain explicit bijections between $ \mathbb{Z} $ -bases for the equivariant cohomology rings of smooth varieties related by an equivariant, proper birational map. We also show that self-intersection classes can be represented as classes of contact loci, under certain restrictions on singularities of subvarieties. We give several applications. Motivated by the relation between self-intersection and contact loci, we define higher-order equivariant multiplicities, generalizing the equivariant multiplicities of Brion and Rossmann; these are shown to be local singularity invariants, and computed in some cases. We also present geometric $ \mathbb{Z} $ -bases for the equivariant cohomology rings of a smooth toric variety (with respect to the dense torus) and a partial flag variety (with respect to the general linear group). 相似文献
19.
Monika Ludwig 《Transactions of the American Mathematical Society》2005,357(10):4191-4213
Centroid and difference bodies define equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of contravariant Minkowski valuations and of -Minkowski valuations.
20.
Andrzej Weber 《Proceedings of the American Mathematical Society》2003,131(9):2633-2638
We present a proof that the equivariant intersection cohomology of any complete algebraic variety acted by a connected algebraic group is a free module over .