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1.
A 3-pseudomanifold (briefly 3-pm) is a finite connected simplicial 3-complex in which the link of every vertex is a closed
2-manifold. Such a link issingular if it is not a sphere. It is proved that for a preassigned list Σ of closed 2-manifolds (other than spheres), there is a
3-pm in which the list of singular links is precisely Σ, iff the number of the non-orientable members in Σ with odd genus
is even. Close relationship is found between 3-pms and 3-manifolds with boundary. This yields a simple proof for the 2-dimensional
case of Pontrjagin-Thom’s theorem (i.e., necessary and sufficient condition for a 2-manifold to bound a 3-manifold). The concept
of a 3-pm is generalized to higher dimensions. 相似文献
2.
In this paper we prove that if M is a compact, hyperbolizable 3-manifold, which is not a handlebody, then the Hausdorff dimension of the limit set is continuous
in the strong topology on the space of marked hyperbolic 3-manifolds homotopy equivalent to M. We similarly observe that for any compact hyperbolizable 3-manifold M (including a handlebody), the bottom of the spectrum of the Laplacian gives a continuous function in the strong topology
on the space of topologically tame hyperbolic 3-manifolds homotopy equivalent to M.
Submitted: January 1998. 相似文献
3.
We define link homology in 4-manifolds, and show that it hasa close connection to linking numbers and intersection matricesof 4-manifolds. We also define null-homologous links in 4-manifolds.We give a necessary and sufficient condition for links to benull-homologous in 4-manifolds. This condition implies thatfor any 4-manifold with second Betti number n, there are (n+ 2)-component links which are not nullhomologous in the 4-manifold. 相似文献
4.
Hong Jun Li 《数学学报(英文版)》2001,17(4):697-714
In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to
develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define
a Poisson matrix on the 3-manifold. And using it as an initial date, we give an explicit expression of all the curvatures
for some Riemannian metric. The method is well applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially
the homogeneous spaces of 3-dimensional Lie groups. 相似文献
5.
本文利用可定向3-流形切丛的平凡性,在3维几何上建立了一种整体标架法.对于3-流形上任一整体切标架,定义了一个Poisson矩阵,并给出:Poisson矩阵在标架改变时的变化规律.以Poisson矩阵为原始数据,计算了相应Riemannian度量各种曲率的具体表达式.对于具有常值Poisson矩阵的一类3-流形,这个方法被用来讨论它们的拓扑结构.它们基本上都是3维李群在其离散子群左平移作用下的商空间. 相似文献
6.
There are ten diffeomorphism classes of compact, flat 3-manifolds. It has been conjectured that each of these occurs as the boundary of a 4-manifold whose interior admits a complete, hyperbolic structure of finite volume. This paper provides evidence in support of the conjecture. In particular, each diffeomorphism class of compact, flat 3-manifolds is shown to appear as one of the cusps of a complete, finite-volume, hyperbolic 4-manifold. This is done with a construction that uses special coverings of
3 by 3-balls. A further consequence of the construction is a finer result about the geometric structures which can be induced on cusps of complete, finite-volume, hyperbolic 4-manifolds. Using Mostow's Rigidity Theorem, one can show that not every flat structure occurs in this way. However, the fact that the flat structures induced on cusps of such 4-manifolds are dense in their respective moduli spaces follows from the construction. 相似文献
7.
Jonathan Spreer 《Discrete and Computational Geometry》2014,51(2):394-426
In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types. 相似文献
8.
In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.
9.
In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show
that the Whitehead manifold lacks such a metric, and in fact that
\mathbbR3{\mathbb{R}^3} is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible
noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented
3-manifolds with finitely generated fundamental group allowing such a metric. 相似文献
10.
We introduce twisted Alexander norms of a compact connected orientable 3-manifold with first Betti number greater than one, generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm of a 3-manifold. Using these we completely determine the Thurston norm of many 3-manifolds which are not determined by norms of McMullen and Turaev.
11.
The Cartesian product of a closed, orientable prime geometric 3-manifold and a closed orientable surface is unique except for the case of the Cartesian product of a special class of Seifert manifolds and a torus. The same type of uniqueness holds for stabilization of 3-manifolds by an n-dimensional torus. Cartesian squares of Seifert fibered 3-manifolds are completely classified. 相似文献
12.
Boju Jiang Yi Ni Shicheng Wang 《Transactions of the American Mathematical Society》2004,356(11):4371-4382
Motivated by the study in Morse theory and Smale's work in dynamics, the following questions are studied and answered: (1) When does a 3-manifold admit an automorphism having a knotted Smale solenoid as an attractor? (2) When does a 3-manifold admit an automorphism whose non-wandering set consists of Smale solenoids? The result presents some intrinsic symmetries for a class of 3-manifolds.
13.
Toru Ikeda 《Geometriae Dedicata》2014,170(1):177-183
The aims of this paper is to prove that every closed connected orientable 3-manifold with an orientation-preserving periodic diffeomorphism contains infinitely many, setwise invariant, spatial graphs whose exteriors are hyperbolic 3-manifolds. 相似文献
14.
A contamination in a 3-manifold is an object interpolating between the contact structure and the lamination. Contaminations
seem to provide a link between 3-dimensional contact geometry and the classical topology of 3-manifolds, as described in a
separate paper (Oertel and Świa̧tkowski, Contact structures, σ-confoliations, and contaminations in 3-manifolds. arXiv math.GT/0307177).
In this article we deal with contaminations carried by branched surfaces, giving a sufficient condition for a branched surface
to carry a pure contamination. 相似文献
15.
We show that the map separation property (MSP), a concept due to H.W. Lambert and R.B. Sher, is an appropriate analogue of J.W. Cannon’s disjoint disks property (DDP) for the class of compact generalized 3-manifolds with zero-dimensional singular set, modulo the Poincaré conjecture. Our main result is that the Poincaré conjecture (in dimension three) is equivalent to the conjecture that every X? with the MSP is a topological 3-manifold. 相似文献
16.
17.
In this paper, we first show the global existence of the three-dimensionalCalabi flow on any closed 3-manifold with an arbitrary background metric g
0. Second, we show the asymptotic convergence of a subsequence ofsolutions of the Calabi flow on a closed 3-manifold with Yamabe constant Q < 0 or Q = 0 and Q > 0, up to conformal transformations. With itsapplication, we prove the existence of extremal metrics for quadraticfunctional of scalar curvature on a closed 3-manifold which is served asan extension of the Yamabe problem on closed manifolds. Moreover, theexistence of extremal metrics on complete noncompact 3-manifolds willdiscuss elsewhere. 相似文献
18.
Jonathan A. Hillman 《Israel Journal of Mathematics》1991,75(2-3):277-287
We give criteria for a closed 4-manifold to be homotopy equivalent to the total space of an S1-bundle over a closed 3-manifold. In the aspherical case the conditions are that the Euler characteristic be 0 and that the
fundamental group have an infinite cyclic normal subgroup such that the quotient group has one end and finite cohomological
dimension. Under further assumptions on this quotient group we characterize the total spaces of such bundles over
-or H2 × E1-manifolds and over E3-, Nil3- or Sol3-manifolds up to s-cobordism and homeomorphism respectively. 相似文献
19.
Sally Kuhlmann 《Geometriae Dedicata》2008,131(1):181-211
We consider the existence of simple closed geodesics or “geodesic knots” in finite volume orientable hyperbolic 3-manifolds.
Every such manifold contains at least one geodesic knot by results of Adams, Hass and Scott in (Adams et al. Bull. London
Math. Soc. 31: 81–86, 1999). In (Kuhlmann Algebr. Geom. Topol. 6: 2151–2162, 2006) we showed that every cusped orientable hyperbolic 3-manifold in fact contains infinitely many geodesic
knots. In this paper we consider the closed manifold case, and show that if a closed orientable hyperbolic 3-manifold satisfies
certain geometric and arithmetic conditions, then it contains infinitely many geodesic knots. The conditions on the manifold
can be checked computationally, and have been verified for many manifolds in the Hodgson-Weeks census of closed hyperbolic
3-manifolds. Our proof is constructive, and the infinite family of geodesic knots spiral around a short simple closed geodesic
in the manifold.
相似文献
20.
S. V. Kharitonova 《Journal of Mathematical Sciences》2011,177(5):742-747
In this paper, we study almost C(λ)-manifolds. We obtain necessary and sufficient conditions for an almost contact metric manifold to be an almost C(λ)-manifold. We prove that contact analogs of A. Gray’s second and third curvature identities on almost C(λ)-manifolds hold, while a contact analog of A. Gray’s first identity holds if and only if the manifold is cosymplectic.
It is proved that a conformally flat, almost C(λ)-manifold is a manifold of constant curvature λ. 相似文献