共查询到20条相似文献,搜索用时 15 毫秒
1.
Using the loop orbifold of the symmetric product, we give a formula for the Poincaré polynomial of the free loop space of the Borel construction of the symmetric product. We also show that the Chas-Sullivan orbifold product structure in the homology of the free loop space of the Borel construction of the symmetric product induces a ring structure in the homology of the inertia orbifold of the symmetric product. For a general almost complex orbifold, we define a new ring structure on the cohomology of its inertia orbifold which we call the virtual intersection ring. Finally we show that under Poincaré duality in the case of the symmetric product orbifold, both ring structures are isomorphic. 相似文献
2.
A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold which is locally modeled on the quotient of a connected, open manifold under a finite group of isometries. If all of the isometries used to define the local structures of an entire orbifold are orientation preserving, we call the orbifold locally orientable. We use heat invariants to show that a Riemannian orbifold which is locally orientable cannot be Laplace isospectral to a Riemannian orbifold which is not locally orientable. As a corollary we observe that a Riemannian orbifold that is not locally orientable cannot be Laplace isospectral to a Riemannian manifold. 相似文献
3.
We derive some asymptotic expansion formulas of the Bergman kernel of high tensor powers of an Hermitian orbifold line bundle with mixed curvature tensored with an orbifold vector bundle on a compact symplectic orbifold. In particular, when the orbifold has isolated singularities, we get an explicit formula for the asymptotic expansion of the Bergman kernel in the distribution sense. Finally, by applying our results to the complex case, we get a Riemann–Roch–Kawasaki type formula. 相似文献
4.
Comparing to the Ch-~Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds, we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen~Ruan cup product for the Che-Ruan cohomology. We also prove that under this cup product the direct sum of all dimensional orbifold cohomology groups constitutes a cohomological ring. Finally we calculate two examples. 相似文献
5.
We proved the convergence of a sequence of two-dimensional compact Kähler-Einstein orbifolds with rational quotient singularities and with some uniform bounds on the volumes and on the Euler characteristics of our orbifolds, to a Kähler-Einstein two-dimensional orbifold. Our limit orbifold can have worse singularities than the orbifolds in our sequence. We will also derive some estimates on the norms of the sections of plurianticanonical bundles of our orbifolds in the sequence that we are considering and our limit orbifold. 相似文献
6.
Acta Mathematica Sinica, English Series - In this paper, we consider double ramification cycles with orbifold targets. An explicit formula for double ramification cycles with orbifold targets,... 相似文献
7.
We generalize the Gauss-Bonnet and Poincaré-Hopf theorems to the case of orbifolds with boundary. We present two such generalizations, the first in the spirit of Satake, in which the local data (i.e. integral of the curvature in the case of the Gauss-Bonnet theorem and the index of the vector field in the case of the Poincaré-Hopf theorem) is related to Satake's orbifold Euler-Satake characteristic, a rational number which depends on the orbifold structure.For the second pair of generalizations, we use the Chen-Ruan orbifold cohomology to express the local data in a way which can be related to the Euler characteristic of the underlying space of the orbifold. 相似文献
8.
In this paper, we generalize the construction of the inverse transgression map done by Adem, A., Ruan, Y. and Zhang, B. in [A stringy product on twisted orbifold K-theory. Morfismos, 11, 33 64 (2007)] and give a different proof to the statement that the image of the inverse transgression map for a gerbe with connection over an orbifold is an inner local system on its inertia orbifold. 相似文献
9.
本文给出一种几何的子轨形群胚的定义,还给出了判定子轨形群胚的依据,并证明了紧子轨形群胚的轨形管状邻域、紧辛子轨形群胚的辛邻域和紧Lagrangian子轨形群胚的Lagrangian邻域的存在性. 相似文献
10.
Generalizing toric varieties, we introduce toric Deligne-Mumford stacks. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an application, we prove that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but is not necessarily isomorphic to) the Chow ring of a crepant resolution. 相似文献
11.
An old problem asks whether a Riemannian manifold can be isospectral to a Riemannian orbifold with nontrivial singular set. In this short note we show that under the assumption of Schanuel’s conjecture in transcendental number theory, this is impossible whenever the orbifold and manifold in question are length-commensurable compact locally symmetric spaces of nonpositive curvature associated to simple Lie groups. 相似文献
12.
Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a
Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold
fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which
give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we
obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two
points.
相似文献
13.
We generalize the definition of orbifold elliptic genus and introduce orbifold genera of chromatic level h, using h-tuples rather than pairs of commuting elements. We show that our genera are in fact orbifold invariants, and we prove integrality results for them. If the genus arises from an H∞-map into the Morava-Lubin-Tate theory Eh, then we give a formula expressing the orbifold genus of the symmetric powers of a stably almost complex manifold M in terms of the genus of M itself. Our formula is the p-typical analogue of the Dijkgraaf-Moore-Verlinde-Verlinde formula for the orbifold elliptic genus [R. Dijkgraaf et al., Elliptic genera of symmetric products and second quantized strings Comm. Math. Phys. 185(1) (1997) 197-209]. It depends only on h and not on the genus. 相似文献
14.
Consider a compact symplectic sub-orbifold groupoid S of a compact symplectic orbifold groupoid (X, ω). Let Xa be the weight-a blowup of X along S, and Da = PNa be the exceptional divisor, where N is the normal bundle of S in X. In this paper we show that the absolute orbifold Gromov-Witten theory of Xα can be effectively and uniquely reconstructed from the absolute orbifold Gromov-Witten theories of X, S and Dα, the natural restriction homomorphism H*CR(X) → H*CR(S) and the first Chern class of the tautological line bundle over Dα. To achieve this we first prove similar results for the relative orbifold Gromov-Witten theories of (Xα | Dα) and (Nα | Dα). As applications of these results, we prove an orbifold version of a conjecture of Maulik and Pandharipande (Topology, 2006) on the Gromov-Witten theory of blowups along complete intersections, a conjecture on the Gromov-Witten theory of root constructions and a conjecture on the Leray-Hirsch result for the orbifold Gromov-Witten theory of Tseng and You (J Pure Appl Algebra, 2016). 相似文献
15.
Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a consequence we obtain the result that every orbifold groupoid is Morita equivalent to the translation groupoid of an almost free action of a proper bundle of topological groups. 相似文献
16.
The BersGreenberg theorem tells us that the Teichmüllerspace of a Riemann surface with branch points (orbifold) dependsonly on the genus and the number of special points, and noton the particular ramification values. On the other hand, theMaskit embedding provides a mapping from the Teichmüllerspace of an orbifold, into the product of one-dimensional Teichmüllerspaces. In this paper we prove that there is a set of isomorphismsbetween one-dimensional Teichmüller spaces that, when restrictedto the image of the Teichmüller space of an orbifold underthe Maskit embedding, provides the BersGreenberg isomorphism. 相似文献
17.
In this paper, we prove the existence of nilpotent Killing structures and F-structures on collapsed Riemannian orbifolds. Therefore a sufficiently collapsed orbifold X is the union of orbits, each orbit is an infranil orbifold of positive dimension; in particular, the F-structure provides a decomposition of X into compact flat orbifolds. 相似文献
18.
We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary
homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application
we consider orbifolds as groupoids and study the notion of orbifold 1-homotopy type induced by a 1-homotopy between presentations
of the orbifold maps. 相似文献
19.
We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a criterion for the non-positivity of it. Moreover, we give a sufficient condition for the equality in the inequality. In order to prove it, we also solve the orbifold Yamabe problem under a certain condition. We use these results to give some exact computations of the Yamabe invariant of compact orbifolds. 相似文献
20.
In this paper, by using the de Rham model of Chen–Ruan cohomology, we define the relative Chen–Ruan cohomology ring for a pair of almost complex orbifold(G, H) with H being an almost sub-orbifold of G. Then we use the Gromov–Witten invariants ofG, the blow-up of G along H,to give a quantum modification of the relative Chen–Ruan cohomology ring H*CR(G, H) when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G. 相似文献
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