共查询到20条相似文献,搜索用时 31 毫秒
1.
We introduce two related concepts for smooth actions of compact Lie groups:The homogeneity rank is a simple numerical invariant of the action.As one of our results we determine the precise range of this invariantfor isometric actions on compact Riemannian manifolds with positivesectional curvature and exhibit special properties of the actionswith maximal homogeneity rank.Atoms are special components of fixed point sets. They inherit actionswith the same cohomogenity and homogeneity rank as the original action,but with trivial principal isotropy group. Other properties of the originalaction like polarity are reflected in the atoms.We determine the atoms in some interesting concrete cases.Not only for this purpose we give a detailed treatise on the structureof fixed point sets, in particular in cohomogeneity one manifolds. 相似文献
2.
Certain Stiefel-Whitney classes of manifolds with smooth, effective toral actions are shown to be computable in terms of Poincare duals of fixed point sets of isotropy subgroups. As an application the toral degrees of symmetry of certain Dold manifolds are determined. 相似文献
3.
In this article, we deal with the following two questions. For smooth actions of a given finite group G on spheres S, which smooth manifolds F occur as the fixed point sets in S, and which real G-vector bundles ν over F occur as the equivariant normal bundles of F in S? We focus on the case G is an Oliver group and answer both questions under some conditions imposed on G, F, and ν. We construct smooth actions of G on spheres by making use of equivariant surgery, equivariant thickening, and Oliver's equivariant bundle extension method modified by an equivariant wegde sum construction and an equivariant bundle subtraction procedure. 相似文献
4.
Krzysztof Pawałowski 《Mathematische Annalen》2008,341(4):845-858
We construct for the first time smooth circle actions on highly symmetric manifolds such as disks, spheres, and Euclidean
spaces which contain two points with the same isotropy subgroup whose representations determined on the tangent spaces at
the two points are not isomorphic to each other. This allows us to answer negatively a question of Hsiang and Hsiang [Some
Problems in Differentiable Transformation Groups, Springer, Berlin, Problem 16, p. 228, 1968].
Dedicated to Prof. Yasuhiko Kitada on the occasion of his 60th birthday.
Krzysztof Pawałowski was supported in part by the KBN Research Grant N 201 008 31/0524. 相似文献
5.
Erkki Laitinen Masaharu Morimoto Krzysztof Pawaŀowski 《Commentarii Mathematici Helvetici》1995,70(1):10-38
The paper presents a method which allows to construct smooth finite nonsolvable group actions on spheres with prescribed fixed
point data. The idea is to consider an action on a disk with the required fixed point data, and then to apply equivariant
surgery to the equivariant double of the disk to remove the second copy of the fixed point data. In this paper, the method
is applied to construct smooth group actions on spheres with exactly one fixed point, and more general actions with fixed
point set diffeomorphic to any given closed stably parallelizable smooth manifold. The method is expected to be useful for
constructions of smooth group actions on spheres with more complicated fixed point data.
1991Mathematics Subject Classification: 57S17, 57S25, 57R67, 57R85. 相似文献
6.
Yi Lin 《Advances in Mathematics》2007,208(2):699-709
In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces. 相似文献
7.
L. Godinho 《Transactions of the American Mathematical Society》2006,358(11):4919-4933
A theorem of Tolman and Weitsman states that all symplectic semifree circle actions with isolated fixed points on compact symplectic manifolds must be Hamiltonian and have the same equivariant cohomology and Chern classes of equipped with the standard diagonal circle action. In this paper, we show that the situation is much different when we consider compact symplectic orbifolds. Focusing on -orbifolds with isolated cone singularities, we show that such actions, besides being Hamiltonian, can now be obtained from either or a weighted projective space, or a quotient of one of these spaces by a finite cyclic group, by a sequence of special weighted blow-ups at fixed points. In particular, they can have any number of fixed points.
8.
Laurent Meersseman 《Mathematische Annalen》2000,317(1):79-115
We consider holomorphic linear foliations of dimension m of (with ) fulfilling a so-called weak hyperbolicity condition and equip the projectivization of the leaf space (for the foliation
restricted to an adequate open dense subset) with a structure of compact, complex manifold of dimension . We show that, except for the limit-case where we obtain any complex torus of any dimension, this construction gives non-symplectic manifolds, including the previous
examples of Hopf, Calabi-Eckmann, Haefliger (linear case), Loeb-Nicolau (linear case) and López de Medrano-Verjovsky. We study
some properties of these manifolds, that is to say meromorphic functions, holomorphic vector fields, forms and submanifolds.
For each manifold, we construct an analytic space of deformations of dimension and show that, under some additional conditions, it is universal. Lastly, we give explicit examples of new compact, complex
manifolds, in particular of connected sums of products of spheres and show the existence of a momentum-like map which classifies
these manifolds, up to diffeomorphism.
Received: 28 October 1998 / in final form: 7 September 1999 相似文献
9.
D. V. Treshchev 《Mathematical Notes》1997,61(6):744-757
Generally, the invariant Lagrangian manifolds (stable and unstable separatrices) asymptotic with respect to a hyperbolic torus
of a Hamiltonian system do not coincide. This phenomenon is called separatrix splitting. In this paper, a symplectic invariant
qualitatively describing separatrix splitting for hyperbolic tori of maximum (smaller by one than the number of degrees of
freedom) dimension is constructed. The construction resembles that of the homoclinic invariant found by lazutkin for two-dimensional
symplectic maps and of Bolotin's invariant for splitting of asymptotic manifolds of a fixed point of a symplectic diffeomorphism.
Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 890–906, June, 1997.
Translated by O. V. Sipacheva 相似文献
10.
D. Kotschick 《Mathematische Zeitschrift》2006,252(1):19-25
We prove that closed symplectic four-manifolds do not admit any smooth free circle actions with contractible orbits, without
assuming that the actions preserve the symplectic forms. In higher dimensions such actions by symplectomorphisms do exist,
and we give explicit examples based on the constructions of FGM. 相似文献
11.
12.
Krzysztof Pawaowski 《K-Theory》1998,13(1):41-55
The paper presents a procedure for constructing smooth actions of finite perfect groups on spheres with fixed point sets having certain prescribed properties (Theorem A); in particular, having any prescribed configuration of Chern and Pontryagin numbers (Corollary C). The main ingredients used are equivariant thickening and equivariant surgery. 相似文献
13.
Ya. A. Prykarpats’kyi 《Ukrainian Mathematical Journal》2006,58(5):763-778
We develop a new approach to the study of properties of ergodic measures for nonautonomous periodic Hamiltonian flows on symplectic
manifolds, which are used in many problems of mechanics and mathematical physics. Using Mather’s results on homologies of
invariant probability measures that minimize some Lagrangian functionals and the symplectic theory developed by Floer and
others for the investigation of symplectic actions and transversal intersections of Lagrangian manifolds, we propose an analog
of a Mather-type β-function for the study of ergodic measures associated with nonautonomous Hamiltonian systems on weakly
exact symplectic manifolds. Within the framework of the Gromov-Salamon-Zehnder elliptic methods in symplectic geometry, we
establish some results on stable and unstable manifolds for hyperbolic invariant sets, which are used in the theory of adiabatic
invariants of slowly perturbed integrable Hamiltonian systems.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 675–691, May, 2006. 相似文献
14.
This article presents several new constructions of infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic. While the construction gives strong evidence that any two of these manifolds of are not diffeomorphic, they cannot be distinguished by Seiberg-Witten invariants. Whether these manifolds are, or are not, diffeomorphic seems to be a very difficult question to answer. For one of these constructions, each member of the family is symplectic with the further property that each contains nullhomologous tori with the property that infinitely many log transformations on these tori yield nonsymplectic 4-manifolds. This is detected by calculations of Seiberg-Witten invariants. The surgery in question can be performed on any 4-manifold which contains as a codimension 0 submanifold a punctured surface bundle over a punctured surface and a nontrivial loop in the base which has trivial monodromy. A starting point for another class of examples in this paper is a family of examples which show that the Parshin-Arakelov theorem for holomorphic Lefschetz fibrations is false in the symplectic category. Such families are constructed by means of knot surgery on ellipitic surfaces. It is shown that for a fixed homeomorphism type X (of a simply connected elliptic surface) and a fixed integer g?3, there are infinitely many genus g Lefschetz fibrations on nondiffeomorphic 4-manifolds, all homeomorphic to X. 相似文献
15.
Anand DESSAI 《Frontiers of Mathematics in China》2016,11(5):1151-1187
We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry. 相似文献
16.
Ana Cannas da Silva Yael Karshon Susan Tolman 《Transactions of the American Mathematical Society》2000,352(2):525-552
We prove several versions of ``quantization commutes with reduction' for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.
17.
Mikiya Masuda Seonjeong Park 《Proceedings of the Steklov Institute of Mathematics》2014,286(1):308-323
The notion of a toric origami manifold, which weakens the notion of a symplectic toric manifold, was introduced by A. Cannas da Silva, V. Guillemin and A.R. Pires. They showed that toric origami manifolds bijectively correspond to origami templates via moment maps, where an origami template is a collection of Delzant polytopes with some folding data. Like a fan is associated to a Delzant polytope, a multi-fan introduced by A. Hattori and M. Masuda can be associated to an oriented origami template. In this paper, we discuss their relationship and show that any simply connected compact smooth 4-manifold with a smooth action of T 2 can be a toric origami manifold. We also characterize products of even dimensional spheres which can be toric origami manifolds. 相似文献
18.
We consider a generalization of Einstein–Sasaki manifolds, which we characterize in terms both of spinors and differential
forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable
examples in seven dimensions. Then, we consider circle actions that preserve the structure and determine conditions for the
contact reduction to carry an induced structure of the same type. We apply this construction to obtain a new hypo-contact
structure on S
2 × T
3. 相似文献
19.
We complete the reduction of Sasakian manifolds with the non-zero case by showing that Willett's contact reduction is compatible with the Sasakian structure. We then prove the compatibility of the non-zero Sasakian (in particular, contact) reduction with the reduction of the Kähler (in particular, symplectic) cone. We provide examples obtained by toric actions on Sasakian spheres and make some comments concerning the curvature of the quotients. 相似文献
20.
Reinhard Schultz 《manuscripta mathematica》1985,51(1-3):171-199
If p is an odd prime and F is the fixed point set of a smooth Zp action on Sn or Dn, then F is a smooth manifold with a unitary structure. Conversely; most Zp homology disks or spheres with unitary structures are fixed point sets of smooth Zp actions on Dn or Sn for suitable n. The results of this paper show that an arbitrary oriented mod p homology disk or sphere is the fixed point set of a smooth Zp action on some Z[l/2]-homology disk or sphere. This result is in general the best possible.Partially supported by NSF Grants MCS 81-04852 and MCS 83-00669 相似文献