共查询到20条相似文献,搜索用时 31 毫秒
1.
Tomasz Rybicki 《Geometriae Dedicata》2011,151(1):175-186
It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold (being
the interior of a compact manifold) are bounded. It follows that these groups are uniformly perfect. In order to characterize
the boundedness several conditions on automorphism groups of an open manifold are introduced. In particular, it is shown that
the commutator length diameter of the automorphism group D(M){\mathcal{D}(M)} of a portable manifold M is estimated by 4. 相似文献
2.
The purpose of this paper is to investigate the properties of presemiclosed mappings and improve some already established results. Moreover, it is shown that, if the domain space isT
0, then optimal continuity and homeomorphism coincide (Theorem 4.18). 相似文献
3.
§ 1 IntroductionThispaperisthesequelto[1 ,2 ].Cairnsetal.[1] introducedthenotionofachaoticgroupactionasageneralizationofchaoticdynamicalsystems(seedefinitionbelow) .Theyshowedthatthecircledoesnotadmitachaoticactionofanygroup ,andconstructedachaoticactionofG =Z×… 相似文献
4.
Ruchi Das 《Periodica Mathematica Hungarica》1995,31(2):123-130
Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological groupG acts is introduced. Some conditions are determined under which expansiveness onX impliesG-expansiveness. A characterization of aG-expansive homeomorphism is obtained which in turn gives a sufficient condition for the homeomorphic extension of aG-expansive homeomorphism to beG-expansive. At the end, some results are stated in the form of concluding remarks. 相似文献
5.
Stable equivalence preserves representation type 总被引:1,自引:0,他引:1
H. Krause 《Commentarii Mathematici Helvetici》1997,72(2):266-284
Given two finite dimensional algebras and , it is shown that is of wild representation type if and only if is of wild representation type provided that the stable categories of finite dimensional modules over and $\Gamma$ are equivalent. The proof uses generic modules. In fact, a stable equivalence induces a bijection between the
isomorphism classes of generic modules over and , and the result follows from certain additional properties of this bijection. In the second part of this paper the Auslander-Reiten
translation is extended to an operation on the category of all modules. It is shown that various finiteness conditions are
preserved by this operation. Moreover, the Auslander-Reiten translation induces a homeomorphism between the set of non-projective
and the set of non-injective points in the Ziegler spectrum. As a consequence one obtains that for an algebra of tame representation
type every generic module remains fixed under the Auslander-Reiten translation.
Received: July 24, 1996 相似文献
6.
David I. Adu 《Geometriae Dedicata》1988,27(2):227-240
In this paper, we calculate the number, up to homeomorphism, of a certain type of dendrites of order 3. This problem arises out of an attempt to characterize certain congruences of S(X), the semigroup of continuous self maps of a topological space X. The dendrites D under consideration are those which satisfy the condition that for each branch point b of D at least one of the components of D — {b} is either an arc or a triod. To facilitate our calculation we first show that each of such dendrites is homeomorphic to one of an apparently more restricted class. We then classify the dendrites into homeomorphism classes and finally calculate the number of such classes. 相似文献
7.
S. G. Dani 《Israel Journal of Mathematics》1982,43(1):62-74
We study the dynamics of projective transformations and apply it to (i) prove that the isotropy subgroups of probability measures
on algebraic homogeneous spaces are algebraic and to (ii) study the class of ergodic quasi-invariant measures of automorphisms
of non-compact Lie groups. It is shown that their support is always a proper subset and that under certain conditions on the
Lie group the induced homeomorphism of the support is topologically equivalent to a translation of a compact group. 相似文献
8.
关于L-fuzzy拓扑分离性的弱同胚不变性质 总被引:4,自引:0,他引:4
本文研究了一种新的弱同胚不变性质,它更具有一般性;证明了目前文献中所论述的各种分离性都是弱同胚不变性质,并且否定回答了王国俊提出的两个分离性问题。 相似文献
9.
Patrice Le Calvez 《Proceedings of the American Mathematical Society》2001,129(11):3221-3230
Using the notion of free transverse triangulation we prove that the rotation number of a given probability measure invariant by a homeomorphism of the open annulus depends continuously on the homeomorphism under some boundedness conditions.
10.
Marc Lackenby 《Geometriae Dedicata》2004,109(1):139-145
Let M and M′ be simple 3-manifolds, each with connected boundary of genus at least two. Suppose that Mand M′ are glued via a homeomorphism between their boundaries. Then we show that, provided the gluing homeomorphism is ‘sufficiently complicated’, the Heegaard genus of the amalgamated manifold is completely determined by the Heegaard genus of Mand M′ and the genus of their common boundary. Here, a homeomorphism is ‘sufficiently complicated’ if it is the composition of a homeomorphism from the boundary ofM to some surface S, followed by a sufficiently high power of a pseudo-Anosov onS, followed by a homeomorphism to the boundary of M′. The proof uses the hyperbolic geometry of the amalgamated manifold, generalised Heegaard splittings and minimal surfaces. 相似文献
11.
O. Ya. Viro 《Journal of Mathematical Sciences》1979,12(1):86-96
In this paper, new examples of nonhomeomorphic knots and links which for certain r have homeomorphic r-sheeted cyclic branched coverings are constructed. In particular, it is proved that the two nonhomeomorphic knots with eleven crossings and with Alexander polynomial equal to one, have homeomorphic two-sheeted branched coverings, and that knots obtained from any knot by the Zeeman construction with p-fold and with q-fold twist have homeomorphic r-sheeted cyclic branched coverings ifp=±q(mod 2r). The construction of examples is based on regluing a link along a submanifold of codimension 1 by means of a homeomorphism which is covered by a homeomorphism which is isotopic to the identity only through nonprojecting isotopies.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 66, pp. 133–147, 1976. 相似文献
12.
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14.
John Franks 《Inventiones Mathematicae》1992,108(1):403-418
Summary We show that an area preserving homeomorphism of the open or closed annulus which has at least one periodic point must in fact have infinitely many interior periodic points. A consequence is the theorem that every smooth Riemannian metric onS
2 with positive Gaussian curvature has infinitely many distinct closed geodesics.In this paper we investigate area preserving homeomorphisms of the annulus and their periodic points. The main result is that an area preserving homeomorphism of the annulus which has at least one periodic point (perhaps on the boundary) must in fact have infinitely many interior periodic points.The motivation and main application of this result is the furthering of a program begun by Birkhoff [B] in his book Dynamical Systems. There he shows that for many Riemannian metrics onS
2, including those with positive curvature, the problem of finding closed geodesics reduces to finding periodic points of a certain area preserving homeomorphism of the annulus. The annulus map in question can be shown to have a periodic point so our main result above can be applied to show the existence of infinitely many distinct closed geodesics whenever this annulus map exists. This is done in Sect. 4 Other quite different approaches to the problem of finding infinitely many geodesics have been successful in handling the cases which do not reduce to the investigation of an annulus homeomorphism (see [Ba]).Oblatum 20-III-1991 & 6-XI-1991 相似文献
15.
Jun Tomiyama 《Acta Appl Math》2009,108(3):561-572
For the homeomorphism C*-algebra A(Σ) arising from a topological dynamical system Σ=(X,σ) where σ is a homeomorphism on an arbitrary compact Hausdorff space X, we first give detailed classification of its closed ideals into four classes. In case when X is a compact metric space, we then determine the conditions when the quotient algebras of A(Σ) become quasidiagonal. The case of A(Σ) itself was treated by M. Pimsner. 相似文献
16.
Qiuxia Liu 《Archiv der Mathematik》2010,94(2):165-171
In this note we consider random C
0 homeomorphism perturbations of a hyperbolic set of a C
1 diffeomorphism. We show that the hyperbolic set is semi-stable under such perturbations, in particular, the topological entropy
will not decrease under such perturbations. 相似文献
17.
Masahiro Shiota 《Inventiones Mathematicae》2014,196(1):163-232
Milnor discovered two compact polyhedra which are homeomorphic but not PL homeomorphic (a counterexample to the Hauptvermutung). He constructed the homeomorphism by a finite procedure repeated infinitely often. Informally, we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times. In this sense, Milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra. In the case where the homeomorphism is semialgebraic, the author and Yokoi proved that the polyhedra in R n are PL homeomorphic. In that article, the required PL homeomorphism was not constructively defined from the given homeomorphism. In the present paper we obtain the PL homeomorphism by a constructive procedure starting from the homeomorphism. We prove in fact that for any ordered field R equipped with any o-minimal structure, two definably homeomorphic compact polyhedra in R n are PL homeomorphic (the o-minimal Hauptvermutung theorem 1.1). Together with the fact that any compact definable set is definably homeomorphic to a compact polyhedron we can say that o-minimal topology is “tame”. 相似文献
18.
The main result of this paper gives a topological property satisfied by any homeomorphism of the annulus
\mathbb A = \mathbb S1 ×[-1, 1]{\mathbb {A} = \mathbb {S}^1 \times [-1, 1]} isotopic to the identity and with at most one fixed point. This generalizes the classical Poincaré-Birkhoff theorem because
this property certainly does not hold for an area preserving homeomorphism h of
\mathbb A{\mathbb {A}} with the usual boundary twist condition. We also have two corollaries of this result. The first one shows in particular that
the boundary twist assumption may be weakened by demanding that the homeomorphism h has a lift H to the strip
[(\mathbbA)\tilde] = \mathbbR ×[-1, 1]{\tilde{\mathbb{A}} = \mathbb{R} \times [-1, 1]} possessing both a forward orbit unbounded on the right and a forward orbit unbounded on the left. As a second corollary we
get a new proof of a version of the Conley–Zehnder theorem in
\mathbb A{\mathbb {A}} : if a homeomorphism of
\mathbb A{\mathbb {A}} isotopic to the identity preserves the area and has mean rotation zero, then it possesses two fixed points. 相似文献
19.
This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hlder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained. 相似文献
20.
具有渐近平均跟踪性质的系统 总被引:1,自引:0,他引:1
牛应轩 《高校应用数学学报(A辑)》2007,22(4):462-468
简记渐近平均跟踪性质为AASP.对于紧致度量空间上的连续映射f,证明了:(1)f有AASP当且仅当其逆极限空间上的移位映射有AASP;(2)若f有AASP且是等度连续的,则f是极小同胚.此外,讨论了AASP的拓扑共轭不变性. 相似文献