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1.
Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism
groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.
This research was partially supported by Grant-in-Aid for Scientific Research (No. 16540058), Japan Society for the Promotion
of Science.
This research was partially supported by Grant-in-Aid for Scientific Research (No. 14540093), Japan Society for the Promotion
of Science. 相似文献
2.
Yukihiro Tsutsumi 《Mathematische Zeitschrift》2004,246(1-2):167-175
A method for constructing hyperbolic knots each of which bounds accidental incompressible Seifert surfaces of arbitrarily high genus is given.
Mathematics Subject Classification (2000):57N10, 57M25.The author was supported in part by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. 相似文献
3.
This paper concerns the problem of irreducible decompositions of unitary representations of topological groups G, including the group Diff0(M) of diffeomorphisms with compact support on smooth manifolds M. It is well known that the problem is affirmative, when G is a locally compact, separable group (cf. [3, 4]). We extend this result to infinite-dimensional groups with appropriate
quasi-invariant measures, and, in particular, we show that every continuous unitary representation of Diff0(M) has an irreducible decomposition under a fairly mild condition.
This research was partially supported by a Grant-in-Aid for Scientific Research (No.14540167), Japan Socieity of the Promotion
of Science. 相似文献
4.
We exhibit strong constraints on the geometry and topology of a uniformly quasiconformally homogeneous hyperbolic manifold. In particular, if n3, a hyperbolic n-manifold is uniformly quasiconformally homogeneous if and only if it is a regular cover of a closed hyperbolic orbifold. Moreover, if n3, we show that there is a constant Kn>1 such that if M is a hyperbolic n-manifold, other than which is K–quasiconformally homogeneous, then KKn.Mathematics Subject Classification (2000): 30C60Research supported in part by NSF grant 070335 and 0305704.Research supported in part by NSF grant 0203698.Research supported in part by the NZ Marsden Fund and the Royal Society (NZ).Research supported in part by NSF grant 0305704. 相似文献
5.
We show that for any possible Weierstrass gap sequence L on a non-singular curve of genus 8 with twice the smallest positive non-gap is less than the largest gap there exists a pointed
non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the Weierstrass gap sequence at P is L. Combining this with the result in [6] we see that every possible Weierstrass gap sequence of genus 8 is attained by some
pointed non-singular curve.
*Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science.
**Partially supported by Grant-in-Aid for Scientific Research (17540030), Japan Society for the Promotion of Science. 相似文献
6.
Haseo Ki 《The Ramanujan Journal》2008,17(1):123-143
The analogue of the Riemann hypothesis for the Ramanujan zeta function states that all zeros of the Ramanujan Ξ-function have real zeros only. We study the zeros of approximations of the Ramanujan Ξ-function.
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion
Fund) (KRF-2006-312-C00021). 相似文献
7.
Dorothee Schueth 《Mathematische Zeitschrift》2008,260(3):595-613
We construct a pair of compact, eight-dimensional, two-step Riemannian nilmanifolds M and M′ which are isospectral for the Laplace operator on functions and such that M has completely integrable geodesic flow in the sense of Liouville, while M′ has not. Moreover, for both manifolds we analyze the structure of the submanifolds of the unit tangent bundle given by two
maximal continuous families of closed geodesics with generic velocity fields. The structure of these submanifolds turns out
to reflect the above (non)integrability properties. On the other hand, their dimension is larger than that of the Lagrangian
tori in M, indicating a degeneracy which might explain the fact that the wave invariants do not distinguish an integrable from a nonintegrable
system here. Finally, we show that for M, the invariant eight-dimensional tori which are foliated by closed geodesics are dense in the unit tangent bundle, and that
both M and M′ satisfy the so-called Clean Intersection Hypothesis.
The author was partially supported by DFG Sonderforschungsbereich 647. 相似文献
8.
9.
Kazuo Akutagawa 《Mathematische Zeitschrift》2003,243(1):85-98
For a supergroup , we describe an obstruction to the existence of positive scalar curvature metrics with minimal boundary condition on a compact
n-dimensional -manifold W with nonempty boundary M, , in terms of the bordism class [M] in the Stolz obstruction group associated to [St2]. In par ticular, when W is a 5-dimensional spin manifold and the -invariant of a connected component of M is nonzero, we prove that W does not admit a positive scalar curvature metric with minimal boundary condition.
Received: 4 July 2001; in final form: 5 February 2002 / Published online: 8 November 2002
RID="*"
ID="*" Partially supported by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No.
11640070. 相似文献
10.
In this paper, we study closed k-maximal spacelike hypersurfaces M
n
in anti-de Sitter space H
1
n+1 (−1) with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
The first author was supported by Japan Society for Promotion of Science. The third author was supported by grant Proj. No.
R17-2008-001-01000-0 from Korea Science & Engineering Foundation. 相似文献
11.
Gaven J. Martin 《Commentarii Mathematici Helvetici》1996,71(1):339-361
We exhibit an interesting new phenomenon concerning certain triangle subgroups Δ of Kleinian groups Γ. Namely the hyperbolic
plane Π stabilized by Δ has a precisely invariant tubular neighbourhood. Thus the corresponding 2-orbifoldF
2=∏/Γ
∏
is always embedded in the hyperbolic 3-orbifoldM
3=ℍ3/Γ. We deduce that any two such triangle groups can algebraically intersect only in a finite cyclic subgroup.
We give sharp estimates for the radius of these tubular neighbourhoods and present applications concerning the estimation
of co-volumes of Kleinian groups containing these triangle subgroups.
for J. A. Kalman on the occasion of his 65th birthday
Research supported in part by grants from the Australian Research Council, the New Zealand Foundation for Research Science
and Technology and the U.K. Scientific and Engineering Research Council. 相似文献
12.
Summary. We deal with a perturbation of a hyperbolic integrable Hamiltonian system with n+1 degrees of freedom. The integrable system is assumed to have n -dimensional hyperbolic invariant tori with coincident whiskers (separatrices).
Following Eliasson, we use a geometric approach closely related to the Lagrangian properties of the whiskers, to show that
the splitting distance between the perturbed stable and unstable whiskers is the gradient of a periodic scalar function of
n phases, which we call splitting potential. This geometric approach works for both the singular (or weakly hyperbolic) case
and the regular (or strongly hyperbolic) case, and provides the existence of at least n+1 homoclinic intersections between the perturbed whiskers.
In the regular case, we also obtain a first-order approximation for the splitting potential, that we call Melnikov potential.
Its gradient, the (vector) Melnikov function, provides a first-order approximation for the splitting distance. Then the nondegenerate
critical points of the Melnikov potential give rise to transverse homoclinic intersections between the whiskers. Generically,
when the Melnikov potential is a Morse function, there exist at least 2
n
critical points.
The first-order approximation relies on the n -dimensional Poincaré-Melnikov method, to which an important part of the paper is devoted. We develop the method in a general
setting, giving the Melnikov potential and the Melnikov function in terms of absolutely convergent integrals, which take into
account the phase drift along the separatrix and the first-order deformation of the perturbed hyperbolic tori. We provide
formulas useful in several cases, and carry out explicit computations that show that the Melnikov potential is a Morse function,
in different kinds of examples.
Received January 18, 1999; final revision received October 25, 1999; accepted December 12, 1999 相似文献
13.
The sum of the total curvatures of two orientable orthogonal foliations on the unit sphereS
2⊂R
3 is at least 4Π. The total curvature of a foliation with saddle singularities on a closed hyperbolic surfaceM is at least (12 Log 2–6 Log 3) ... |χ(M)|.
相似文献
14.
Xiaodong Wang 《Journal of Geometric Analysis》2008,18(1):272-284
Let (M
n
,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ
0 of its universal covering satisfies λ
0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy.
The author was partially supported by NSF Grant 0505645. 相似文献
15.
A. P. Pozhidaev 《Siberian Mathematical Journal》2005,46(4):717-721
A root decomposition is constructed of the simple eight-dimensional ternary Malcev algebra M
8. In result, M
8 is equipped with a structure of a Z
3-graded ternary algebra.Original Russian Text Copyright © 2005 Pozhidaev A. P.The author was supported by the Russian Science Support Foundation and partially by the Russian Foundation for Basic Research (Grant 05-01-00230).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 901–906, July–August, 2005. 相似文献
16.
We show that two C*-algebraic noncommutative tori are strongly Morita equivalent if and only if they have isomorphic ordered K
0-groups and centers, extending N. C. Phillips’s result in the case that the algebras are simple. This is also generalized
to the twisted group C*-algebras of arbitrary finitely generated abelian groups.
This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada, held by George
A. Elliott. 相似文献
17.
Danny Calegari 《Geometric And Functional Analysis》2008,18(1):50-76
This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive ϵ there is a positive δ depending only on n and on ϵ such that an element of π1(M) with stable commutator length less than δ is represented by a geodesic with length less than ϵ. Moreover, for any such M, the first accumulation point for stable commutator length on conjugacy classes is at least 1/12.
Conversely, “most” short geodesics in hyperbolic 3-manifolds have arbitrarily small stable commutator length. Thus stable
commutator length is typically good at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a kind of
homological Margulis constant.
Received: June 2006 Revision: May 2007 Accepted: June 2007 相似文献
18.
We prove the following theorem for a finitely generated field K: Let M be a Galois extension of K which is not separably closed. Then M is not PAC over K.
Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation.
This work constitutes a part of the Ph.D. dissertation of L. Bary-Soroker done at Tel Aviv University under the supervision
of Prof. Dan Haran. 相似文献
19.
Junya Takahashi 《manuscripta mathematica》2006,121(2):191-200
We prove that the eigenvalues of the Laplacian acting on functions converge to those of the limit manifold for a special collapsing family of closed Riemannian manifolds without curvature bounds. The proof uses L
2-analysis.Dedicated to Professor Hajime Urakawa on his sixtieth birthday.The author is partially supported by the Grant-in-Aid for Scientific Research No. 16740026 of the Japan Society for the Promotion of Science. 相似文献
20.
Ara Basmajian 《Inventiones Mathematicae》1994,117(1):207-225
Summary We show that a closed embedded totally geodesic hypersurface in a hyperbolic manifold has a tubular neighborhood whose width only depends on the area of the hypersurface. Namely, we construct a tubular neighborhood function and show that an embedded closed totally geodesic hypersurface in a hyperbolic manifold has a tubular neighborhood whose width only depends on the area of the hypersurface (and hence not on the geometry of the ambient manifold). The implications of this result for volumes of hyperbolic manifolds is discussed. In particular, we show that ifM is a hyperbolic 3-manifold containingn rank two cusps andk disjoint totally geodesic embedded closed surfaces, then the volume ofM is bigger than
. We also derive a (hyperbolic) quantitative version of the Klein-Maskit combination theorem (in all dimensions) for free products of fuchsian groups. Using this last result, we construct examples to illustrate the qualitative sharpness of our tubular neighborhood function in dimension three. As an application of our results we give an eigenvalue estimate.Oblatum IX-1992 & 18-VIII-1993Research supported in part by NSF Grant DMS-9207019 相似文献