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1.
Consider a symplectic form ω and a closed 2-form ω1 on a real or complex manifold. Suppose that the Nijenhuis torsion of the tensor fieldJ defined by ω1(X,Y) = ω(JX,Y) vanishes. In this paper we give the complete local classification of the couple {ω, ω1} on a dense open set, defined by some minor conditions of regularity. Around each point of this open set we can find coordinates on wich ω is written with constant coefficients and ω1 with affine ones. Projet de recherche DGICYT PB91-0412  相似文献   

2.
LetX be a locally compact abelian group and ω(.,.) a symplectic structure on it. A polarization for (X, ω) is a pair of totally isotropic closed subgroupsG, G* ofX such thatX =G.G* and ω(.,.) defines a dual pairing ofG andG*. In this paper we describe a class of such groups which always admit a polarization and also discuss their structure. Dedicated to the memory of Professor K G Ramanathan  相似文献   

3.
We study final group topologies and their relations to compactness properties. In particular, we are interested in situations where a colimit or direct limit is locally compact, a k ω-space, or locally k ω. As a first application, we show that unitary forms of complex Kac-Moody groups can be described as the colimit of an amalgam of subgroups (in the category of Hausdorff topological groups, and the category of k ω-groups). Our second application concerns Pontryagin duality theory for the classes of almost metrizable topological abelian groups, resp., locally k ω topological abelian groups, which are dual to each other. In particular, we explore the relations between countable projective limits of almost metrizable abelian groups and countable direct limits of locally k ω abelian groups.  相似文献   

4.
It is proved that any Σ-group, which is a special elongation of a totally projective abelian p-group by a p ω+1-projective abelian p-group, is totally projective. In particular, each p ω+1-projective abelian Σ-p-group is a direct sum of countable p-groups of lengths not exceeding ω + 1. This strengthens our recent result published in Comment. Math. Univ. St. Pauli (2006). Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 180–185, April–June, 2006.  相似文献   

5.
We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p ω+n -projective group precisely when it is totally projective. In particular, each p-torsion p ω+n -projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7]. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007.  相似文献   

6.
Given a closed connected Riemannian manifold M and a connected Riemannian manifold N, we consider fiberwise, i.e. M×{z}, z ? N{M\times \{z\}, z\in N}, volume non-increasing diffeomorphisms on the product M × N. Our main theorems show that in the presence of a certain cohomological condition on M and N such diffeomorphisms must map a fiber diffeomorphically onto another fiber and are therefore fiberwise volume preserving. As a first corollary, we show that the isometries of M × N split. As a second corollary, we prove a special case of an extension of Talelli’s conjecture.  相似文献   

7.
8.
For a single aperiodic, orientation preserving diffeomorphism on the circle, all known local results on the differentiability of the conjugating map are also known to be global results. We show that this does not hold for commutative groups of diffeomorphisms. Given a set of rotation numbers, we construct commuting diffeomorphisms inC 2-ε for all ε>0 with these rotation numbers that are not conjugate to rotations. On the other hand, we prove that for a commutative subgroupFC 1+β, 0<β<1, containing diffeomorphisms that are perturbations of rotations, a conjugating maph exists as long as the rotation numbers of this subset jointly satisfy a Diophantine condition.  相似文献   

9.
Let ℚ ab denote the maximal abelian extension of the rationals ℚ, and let ℚabnil denote the maximal nilpotent extension of ℚ ab . We prove that for every primep, the free pro-p group on countably many generators is realizable as the Galois group of a regular extension of ℚabnil(t). We also prove that ℚabnil is not PAC (pseudo-algebraically closed). This paper was inspired by the author's participation in a special year on the arithmetic of fields at the Institute for Advanced Studies at the Hebrew University of Jerusalem. I would like to express my appreciation to the Institute for its hospitality, and to the organizers, especially Moshe Jarden. Partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund-Japan Technion Society Research Fund.  相似文献   

10.
Let M be a compact manifold with a symplectic form ω and consider the group Dw{\mathcal{D}_\omega} consisting of diffeomorphisms that preserve ω. We introduce a Riemannian metric on M which is compatible with ω and use it to define an L 2-inner product on vector fields on M. Extending by right invariance we get a weak Riemannian metric on Dw{\mathcal{D}_\omega} . We show that this metric has geodesics which come from integral curves of a smooth vector field on the tangent bundle of Dw{\mathcal{D}_\omega} . Then, estimating the growth of such geodesics, we show that they extend globally.  相似文献   

11.
In this paper, firstly we calculate Picard groups of a nilpotent orbit 𝒪 in a classical complex simple Lie algebra and discuss the properties of being ℚ-factorial and factorial for the normalization 𝒪tilde; of the closure of 𝒪. Then we consider the problem of symplectic resolutions for 𝒪tilde;. Our main theorem says that for any nilpotent orbit 𝒪 in a semi-simple complex Lie algebra, equipped with the Kostant-Kirillov symplectic form ω, if for a resolution π:Z𝒪tilde;, the 2-form π*(ω) defined on π−1(𝒪) extends to a symplectic 2-form on Z, then Z is isomorphic to the cotangent bundle T *(G/P) of a projective homogeneous space, and π is the collapsing of the zero section. It proves a conjecture of Cho-Miyaoka-Shepherd-Barron in this special case. Using this theorem, we determine all varieties 𝒪tilde; which admit such a resolution. Oblatum 6-V-2002 & 7-VIII-2002?Published online: 10 October 2002  相似文献   

12.
Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted L p -space L p (G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for L p (G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and L p (G, ω) is a Banach algebra, then G is σ-compact.  相似文献   

13.
LetG be the discrete group of orientation preserving diffeomorphisms of the circle. An explicit simplicial formula on the level of the bar construction is given for the Euler Class of a circle bundle with structure groupG. An upper bound for the Euler Class is obtained which, when the base space of the bundle is a closed orientable surface, reduces to that of J. Wood. An invariant of circle bundles, complexity, is defined which “detects” the upper bound. Partially supported by a grant from the N.S.F.  相似文献   

14.
We consider a holomorphic 1-form ω with an isolated zero on an isolated complete intersection singularity (V,0). We construct quadratic forms on an algebra of functions and on a module of differential forms associated to the pair (V,ω). They generalize the Eisenbud–Levine–Khimshiashvili quadratic form defined for a smooth V. Partially supported by the DFG-programme 'Global methods in complex geometry' (Eb 102/4–3) grants RFBR–04–01–00762, NSh–1972.2003.1.  相似文献   

15.
We study the class of pseudo-norms on the space of smooth functions on a closed symplectic manifold, which are invariant under the action of the group of Hamiltonian diffeomorphisms. Our main result shows that any such pseudo-norm that is continuous with respect to the C -topology, is dominated from above by the L -norm. As a corollary, we obtain that any bi-invariant Finsler pseudo-metric on the group of Hamiltonian diffeomorphisms that is generated by an invariant pseudonorm that satisfies the aforementioned continuity assumption, is either identically zero or equivalent to Hofer’s metric.  相似文献   

16.
In this paper we count closed orbits of a hyperbolic diffeomorphism restricted to a basic set. In fact we shall be dealing with two types of extensions of a hyperbolic diffeomorphism: a finite group extension (also called G-extensions) and also an automorphism extension (also called (G, ρ)-extensions). In particular we present Chebotarev type theorems and prime orbit theorem for such diffeomorphisms. These counting results are in the form of an asymptotic formula derived in complete analogy with the number theoretic result. The main difficulty is extending the domain of analyticity of the zeta and L-functions and this is overcome by resorting to symbolic dynamics. Unlike the case of a flow, the proof of this extension result does not rely on the properties of the Ruelle–Perron–Frobenius operator. Also the counting results do not use any tauberian theorems. Received: January 7, 2005.  相似文献   

17.
A permutation group on a countably infinite domain is called oligomorphic if it has finitely many orbits of finitary tuples. We define a clone on a countable domain to be oligomorphic if its set of permutations forms an oligomorphic permutation group. There is a close relationship to ω-categorical structures, i.e., countably infinite structures with a first-order theory that has only one countable model, up to isomorphism. Every locally closed oligomorphic permutation group is the automorphism group of an ω-categorical structure, and conversely, the canonical structure of an oligomorphic permutation group is an ω-categorical structure that contains all first-order definable relations. There is a similar Galois connection between locally closed oligomorphic clones and ω-categorical structures containing all primitive positive definable relations. In this article we generalise some fundamental theorems of universal algebra from clones over a finite domain to oligomorphic clones. First, we define minimal oligomorphic clones, and present equivalent characterisations of minimality, and then generalise Rosenberg’s five types classification to minimal oligomorphic clones. We also present a generalisation of the theorem of Baker and Pixley to oligomorphic clones. Presented by A. Szendrei. Received July 12, 2005; accepted in final form August 29, 2006.  相似文献   

18.
The weight-spectrumSp(w, X) of a spaceX is the set of weights of all infinite closed subspaces ofX. We prove that ifκ>ω is regular andX is compactT 2 withω(X)κ then some λ withκ≤λ≤2 is inSp(ω, X). Under CH this implies that the weight spectrum of a compact space can not omitω 1, and thus solves problem 22 of [M]. Also, it is consistent with 2ω=c being anything it can be that every countable closed setT of cardinals less thanc withω ∈ T satisfiesSp(w, X)=T for some separable compact LOTSX. This shows the independence from ZFC of a conjecture made in [AT]. Research supported by OTKA grant no. 1908.  相似文献   

19.
We construct, under MA, a non-Hausdorff (T1-)topological extension *ω of ω, such that every function from ω to ω extends uniquely to a continuous function from *ω to *ω. We also show (in ZFC) that for every nontrivial topological extension *X of a countable set X there exists a topology τf on *X, strictly finer than the Star topology, and such that (*X, τf) is still a topological extension of X with the same function extensions *f. This solves two questions raised by M. Di Nasso and M. Forti.  相似文献   

20.
We construct, under MA, a non-Hausdorff (T1-)topological extension *ω of ω, such that every function from ω to ω extends uniquely to a continuous function from *ω to *ω. We also show (in ZFC) that for every nontrivial topological extension *X of a countable set X there exists a topology τf on *X, strictly finer than the Star topology, and such that (*X, τf) is still a topological extension of X with the same function extensions *f. This solves two questions raised by M. Di Nasso and M. Forti.  相似文献   

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