共查询到20条相似文献,搜索用时 44 毫秒
1.
S. Adams 《Geometric And Functional Analysis》2001,11(2):201-243
If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some x ? X x \in X , the orbit map g ? gx : G ? X g \mapsto gx : G \to X is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G such that G admits a locally faithful, orbit nonproper action on a connected Lorentz manifold. In this paper, we describe three collections of groups such that G admits such an action iff G is in one of the three collections. In an earlier paper, we effectively described the first collection. In yet another paper, we describe effectively those groups in the second collection which are not contained in the union of the first and third. Finally, in another paper, we describe effectively the third collection. 相似文献
2.
Scot Adams 《Geometriae Dedicata》2003,98(1):1-45
If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some xX, the orbit map ggx:GX is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G admitting a locally faithful, orbit nonproper, isometric action on a connected Lorentz manifold. In an earlier paper, we found three collections of groups such that G admits such an action iff G is in one of the three collections. In another paper, we effectively described the first collection. In this paper, we show that the second collection contains a small, effectively described collection of groups, and, aside from those, it is contained in the union of the first and third collections. Finally, in a third paper, we effectively describe the third collection, thus solving the stated problem. 相似文献
3.
Scot Adams 《Geometriae Dedicata》2001,88(1-3):91-112
We prove that, in some situations, an induced action from a normal subgroup preserves a geometric structure. Combined with known geometric rigidity results, this result implies certain rigidity statements concerning the full diffeomorphism group of a manifold. It also provides many examples of actions on Lorentz manifolds. Combining these with a small number of well-known actions, we get the full list of connected, simply connected Lie groups admitting a locally faithful, orbit nonproper action by isometries of a connected Lorentz manifold. We give an example of a connected nilpotent Lie group with no complicated action on a Lorentz manifold. We show that, if a connected Lie group has a normal closed subgroup isomorphic to a (two-dimensional) cylinder, then it admits a locally faithful, orbit nonproper action by isometries of a connected Lorentz manifold. 相似文献
4.
Abdelhak Abouqateb 《manuscripta mathematica》1999,98(3):349-362
The purpose of this paper is to characterise the invariant sections-distributions by a proper action. More precisely, we show
that if G is a connected Lie group acting on a differentiable vector bundle E→V such that the induced action on V is proper, then the topological vector space of the G-invariant linear functionals (on the space of C
∞ sections with compact support) equipped with the induced weak-topology (resp. the strong-topology), is isomorphic to the
weak (resp. strong) topological dual of the space (of all G-invariant sections σ with compact quotient supp(σ)/G) equipped with a suitable topology; this coincides with the
usual C
∞-topology if the orbit space is compact, and with the Schwartz-topology if the group G is compact.
Received: 8 June 1998 / Revised version: 22 September 1998 相似文献
5.
Takahiko Yoshida 《Advances in Mathematics》2011,227(5):1914
We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove that local torus actions are classified topologically by them. As a corollary, we obtain a topological classification of locally standard torus actions, which includes the topological classifications of quasi-toric manifolds by Davis and Januszkiewicz and of effective T2-actions on four-dimensional manifolds without nontrivial finite stabilizers by Orlik and Raymond. We discuss locally toric Lagrangian fibrations from the viewpoint of local torus actions. We also investigate the topology of a manifold equipped with a local torus action when the Euler class of the orbit map vanishes. 相似文献
6.
Hee Oh 《Mathematische Annalen》2001,321(4):789-815
We generalize Margulis's S-arithmeticity theorem to the case when S can be taken as an infinite set of primes. Let R be the set of all primes including infinite one and set . Let S be any subset of R. For each , let be a connected semisimple adjoint -group and be a compact open subgroup for each finite prime . Let denote the restricted topological product of 's, with respect to 's. Note that if S is finite, . We show that if , any irreducible lattice in is a rational lattice. We also present a criterion on the collections and for to admit an irreducible lattice. In addition, we describe discrete subgroups of generated by lattices in a pair of opposite horospherical subgroups.
Received: 30 November 2000 / Revised version: 2 April 2001 / Published online: 24 September 2001 相似文献
7.
We show that every mapping of the first functional Lebesgue class that acts from a topological space into a separable metrizable
space that is linearly connected and locally linearly connected belongs to the first Baire class. We prove that the uniform
limit of functions of the first Baire class ƒ
n: X → Y belongs to the first Baire class if X is a topological space and Y is a metric space that is linearly connected and locally linearly connected.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 568–572, April, 2006. 相似文献
8.
Nicolas Dutertre 《Geometriae Dedicata》2004,105(1):43-59
We establish a Gauss—Bonnet type formula for a smooth fibre of a nonproper real polynomial of
n
. For this we need to study topological properties of a generic hyperplane section of this fibre. 相似文献
9.
The classical Mac Lane-Whitehead equivalence showing that crossed modules of groups are algebraic models of connected homotopy 2-types has found a corresponding equivariant version by Moerdijk and Svensson ([22]). In this paper we show that this equivariant result has a higher-dimensional version which gives an equivalence between the homotopy category of diagrams of certain objects indexed by the orbit category of a group H and H-equivariant homotopy n-types for n1.Supported by DGICYT:PS90-0226 相似文献
10.
Benjamin Steinberg 《Semigroup Forum》2010,81(1):217-227
We associate a 2-complex to the following data: a presentation of a semigroup S and a transitive action of S on a set V by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient
condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results
on presentations of Schützenberger groups. We also give a geometric proof that a finitely generated regular semigroup with
finitely many idempotents has polynomial growth if and only if all its maximal subgroups are virtually nilpotent. 相似文献
11.
We prove that a locally faithful, isometric action of SLn(ℝ) ⋉ ℝn on a connected Lorentz manifold must be a proper action. This provides an essential step toward classifying nonproper isometry
groups of noncompact Lorentz manifolds.
The first author was supported in part by NSF grant DMS-9703480. 相似文献
12.
Claus Scheiderer 《Monatshefte für Mathematik》1984,98(1):75-81
A closed subgroupQ of a topological groupG is called topologically quasinormal (tqn) inG if
holds for every closed subgroupA ofG. We show that every tqn subgroup of a connected locally compact group is actually a normal subgroup. Besides we prove: a homogeneous spaceG/H of a connected Lie groupG with the property that every non-trivial one-parameter orbit is dense has dimension at most one. 相似文献
13.
In this paper, the authors systematically discuss orbit braids in M × I with regards to orbit configuration space FG(M, n), where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G. These orbit braids form a group, named orbit braid group, which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M, n), F(M/G, n) and F(M, n). They also co... 相似文献
14.
Inho Kim 《manuscripta mathematica》1998,97(3):343-352
We prove an optimal relative isoperimetric inequality
for a 2-dimensional minimal surface in the n-dimensional space form of nonpositive constant curvature κ under the assumptions that lies in the exterior of a convex domain and contains a subset Γ which is contained in
and along which meets perpendicularly and that is connected, or more generally radially-connected from a point in Γ. Also we obtain an optimal version of linear isoperimetric
inequalities for minimal submanifolds in a simply connected Riemannian manifolds with sectional curvatures bounded above by
a nonpositive number. Moreover, we show the monotonicity property for the volume of a geodesic ball in such minimal submanifolds.
We emphasize that in all the results of this paper minimal submanifolds need not be area minimizing or even stable.
Received: 7 October 1997 / Revised version: 28 April 1998 相似文献
15.
Peter Wong 《manuscripta mathematica》1999,98(2):243-254
Let f,g:X→M be maps between two closed connected orientable n-manifolds where M=G/K is the homogeneous space of left cosets of a compact connected Lie group G by a finite subgroup K. In this note, we obtain a simple formula for the Lefschetz coincidence number L(f,g) in terms of topological degree, generalizing some previously known formulas for fixed points. Our approach, by means of
Nielsen root theory, also allows us to give a simpler and more geometric proof of the fact that all coincidence classes of
f and g have coincidence index of the same sign.
Received: 3 March 1998 / Revised version: 29 June 1998 相似文献
16.
Victor Gerasimov 《Geometric And Functional Analysis》2009,19(1):137-169
Let a discrete group G act by homeomorphisms of a compactum in a way that the action is properly discontinuous on triples and cocompact on pairs.
We prove that such an action is geometrically finite. The converse statement was proved by P. Tukia [T3]. So, we have another
topological characterisation of geometrically finite convergence groups and, by the result of A. Yaman [Y2], of relatively
hyperbolic groups. Further, if G is finitely generated then the parabolic subgroups are finitely generated and undistorted. This answer to a question of B.
Bowditch and eliminates restrictions in some known theorems about relatively hyperbolic groups.
Received: April 2007, Revision: May 2008, Accepted: August 2008 相似文献
17.
Let G be a connected reductive linear algebraic group over , and X a compact connected Riemann surface. Let be a Levi factor of some parabolic subgroup of G, with its maximal abelian quotient. We prove that a holomorphic G-bundle over X admits a flat connection if and only if for every such L and every reduction of the structure group of to L, the -bundle obtained by extending the structure group of is topologically trivial. For , this is a well-known result of A. Weil.
Received: 1 December 2000 / Revised version: 2 April 2001 / Published online: 24 September 2001 相似文献
18.
In 1995, T. Giordano, I. Putnam, and C. Skau [GPS] made a significant breakthrough in Cantor minimal system theory. They completely
classified Cantor minimal systems in the sense of topological orbit equivalence by using C*-algebra and homological algebra techniques. Since then, a dynamical proof of their theorem has been conjectured. Such a
proof is presented in this paper. We establish orbit equivalence theory based on a finite coordinate change relation arising
from an ordered Bratteli diagram, which is known from [HK] in the finitary case of ergodic probability measure-preserving
transformations. We obtain the Orbital Extension Theorem. This theorem is considered a topological version of the Copying
Lemma of Y. Katznelson and B. Weiss [KW], which has played an important role in measured orbit equivalence theory. 相似文献
19.
20.
The “Projective Rank” of a compact connected irreducible Hermitian symmetric space M has been defined as the maximal complex dimension of the compact totally geodesic complex submanifolds having positive holomorphic bisectional curvature with the induced K?hler metric. We present a geometric way to compute this
invariant for the space M based on ideas developed in [1], [13] and [14]. As a consequence we obtain the following inequality relating the Projective Rank,
the usual rank, and the 2-number (which is known to be equal to the Euler-Poincare characteristic in these spaces).
Received: 6 June 2000 / Revised version: 6 August 2001 / Published online: 4 April 2002 相似文献