共查询到20条相似文献,搜索用时 31 毫秒
1.
C.A. Morales 《Topology and its Applications》2012,159(3):787-790
We prove that an Axiom A vector field on an orientable closed 3-manifold not homeomorphic toS3 for which every transverse torus bounds a solid torus either is transitive or has a sink or a source. This result is false without these hypotheses. 相似文献
2.
Luis G. Valdez-Sánchez 《Topology and its Applications》2007,154(3):584-603
Let M be a compact, connected, orientable, irreducible 3-manifold and T0 an incompressible torus boundary component of M such that the pair (M,T0) is not cabled. By a result of C. Gordon, if (S,∂S),(T,∂T)⊂(M,T0) are incompressible punctured tori with boundary slopes at distance Δ=Δ(∂S,∂T), then Δ?8, and the cases where Δ=6,7,8 are very few and classified. We give a simplified proof of this result (or rather, of its reduction process), using an improved estimate for the maximum possible number of mutually parallel negative edges in the graphs of intersection of S and T. We also extend Gordon's result by allowing either S or T to be an essential Klein bottle. 相似文献
3.
Miwa Iwakura 《Topology and its Applications》2009,156(10):1753-1766
We give a concrete example of an infinite sequence of (pn,qn)-lens spaces L(pn,qn) with natural triangulations T(pn,qn) with pn tetrahedra such that L(pn,qn) contains a certain non-orientable closed surface which is fundamental with respect to T(pn,qn) and of minimal crosscap number among all closed non-orientable surfaces in L(pn,qn) and has n−2 parallel sheets of normal disks of a quadrilateral type disjoint from the pair of core circles of L(pn,qn). Actually, we can set p0=0, q0=1, pk+1=3pk+2qk and qk+1=pk+qk. 相似文献
4.
Violeta Vasilevska 《Topology and its Applications》2006,153(15):2765-2781
Our main interest in this paper is further investigation of the concept of (PL) fibrators (introduced by Daverman [R.J. Daverman, PL maps with manifold fibers, J. London Math. Soc. (2) 45 (1992) 180-192]), in a slightly different PL setting. Namely, we are interested in manifolds that can detect approximate fibrations in the new setting. The main results state that every orientable, special (a new class of manifolds that we introduce) PL n-manifold with non-trivial first homology group is a fibrator in the new category, if it is a codimension-2 fibrator (Theorem 8.2) or has a non-cyclic fundamental group (Theorem 8.4). We show that all closed, orientable surface S with χ(S)<0 are fibrators in the new category. 相似文献
5.
D. König asks the interesting question in [7] whether there are facts corresponding to the theorem of Kuratowski which apply to closed orientable or non-orientable surfaces of any genus. Since then this problem has been solved only for the projective plane ([2], [3], [8]). In order to demonstrate that König’s question can be affirmed we shall first prove, that every minimal graph of the minimal basis of all graphs which cannot be embedded into the orientable surface f of genusp has orientable genusp+1 and non-orientable genusq with 1≦q≦2p+2. Then let f be the torus. We shall derive a characterization of all minimal graphs of the minimal basis with the nonorientable genusq=1 which are not embeddable into the torus. There will be two very important graphs signed withX 8 andX 7 later. Furthermore 19 graphsG 1,G 2, ...,G 19 of the minimal basisM(torus, >4) will be specified. We shall prove that five of them have non-orientable genusq=1, ten of them have non-orientable genusq=2 and four of them non-orientable genusq=3. Then we shall point out a method of determining graphs of the minimal basisM(torus, >4) which are embeddable into the projective plane. Using the possibilities of embedding into the projective plane the results of [2] and [3] are necessary. This method will be called saturation method. Using the minimal basisM(projective plane, >4) of [3] we shall at last develop a method of determining all graphs ofM(torus, >4) which have non-orientable genusq≧2. Applying this method we shall succeed in characterizing all minimal graphs which are not embeddable into the torus. The importance of the saturation method will be shown by determining another graphG 20≠G 1,G 2, ...,G 19 ofM(torus, >4). 相似文献
6.
7.
Let M denote a connected (n+1)-manifold (without boundary). We study laminated decompositions of M, by which we mean upper semicontinous decompositions G of M into closed, connected n-manifolds. In particular, given M with a lamination G and N, a locally flat, closed, n-dimensional submanifold, we determine conditions under which M admits another lamination GN with N?GN. For n ≠ 3 a sufficient condition is that i: N → M be a homotopy equivalence. For n > 3 we give examples to show that i: N → M being a homology equivalence is not sufficient. We also show how to replace the assumption of local flatness of N with a weaker cellularity criterion (n ? 4) known as the inessential loops condition. We then give examples illustrating the abundance of pathology if M is not assumed to have a preexisting lamination. 相似文献
8.
Let M be a compact orientable irreducible 3-manifold, F be an essential non-separating closed surface in M. We denote by η(F) the open regular neighborhood of F. If M−η(F) has a high distance Heegaard splitting, then M has a unique minimal Heegaard splitting up to isotopy. 相似文献
9.
S. Bautista 《Journal of Differential Equations》2008,245(3):637-652
Let X be a vector field in a compact n-manifold M, n?2. Given Σ⊂M we say that q∈M satisfies (P)Σ if the closure of the positive orbit of X through q does not intersect Σ, but, however, there is an open interval I with q as a boundary point such that every positive orbit through I intersects Σ. Among those q having saddle-type hyperbolic omega-limit set ω(q) the ones with ω(q) being a closed orbit satisfy (P)Σ for some closed subset Σ. The converse is true for n=2 but not for n?4. Here we prove the converse for n=3. Moreover, we prove for n=3 that if ω(q) is a singular-hyperbolic set [C. Morales, M. Pacifico, E. Pujals, On C1 robust singular transitive sets for three-dimensional flows, C. R. Acad. Sci. Paris Sér. I 26 (1998) 81-86], [C. Morales, M. Pacifico, E. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers, Ann. of Math. (2) 160 (2) (2004) 375-432], then ω(q) is a closed orbit if and only if q satisfies (P)Σ for some Σ closed. This result improves [S. Bautista, Sobre conjuntos hiperbólicos-singulares (On singular-hyperbolic sets), thesis Uiversidade Federal do Rio de Janeiro, 2005 (in Portuguese)] and [C. Morales, M. Pacifico, Mixing attractors for 3-flows, Nonlinearity 14 (2001) 359-378]. 相似文献
10.
Ayako Ido 《Topology and its Applications》2012,159(4):1106-1114
Suppose a closed orientable 3-manifold M has a genus g Heegaard surface P with distance d(P)=2g. Let Q be another genus g Heegaard surface which is strongly irreducible. Then we show that there is a height function f:M→I induced from P such that by isotopy, Q is deformed into a position satisfying the following; (1) fQ| has 2g+2 critical points p0,p1,…,p2g+1 with f(p0)<f(p1)<?<f(p2g+1) where p0 is a minimum and p2g+1 is a maximum, and p1,…,p2g are saddles, (2) if we take regular values ri (i=1,…,2g+1) such that f(pi−1)<ri<f(pi), then f−1(ri)∩Q consists of a circle if i is odd, and f−1(ri)∩Q consists of two circles if i is even. 相似文献
11.
J.C. Gómez-Larrañaga 《Topology and its Applications》2007,154(7):1363-1367
Motivated by the concept of A-category of a manifold introduced by Clapp and Puppe, we give a different proof of a (slightly generalized) Theorem of Hempel and McMillan: If M is a closed 3-manifold that is a union of three open punctured balls then M is a connected sum of S3 and S2-bundles over S1. 相似文献
12.
Simon A. King 《Topology and its Applications》2007,154(6):1141-1156
Turaev-Viro invariants are defined via state sum polynomials associated to a special spine or a triangulation of a compact 3-manifold. By evaluation of the state sum at any solution of the so-called Biedenharn-Elliott equations, one obtains a homeomorphism invariant of the manifold (“numerical Turaev-Viro invariant”). The Biedenharn-Elliott equations define a polynomial ideal. The key observation of this paper is that the coset of the state sum polynomial with respect to that ideal is a homeomorphism invariant of the manifold (“ideal Turaev-Viro invariant”), stronger than the numerical Turaev-Viro invariants. Using computer algebra, we obtain computational results on several examples of ideal Turaev-Viro invariants, for all closed orientable irreducible manifolds of complexity at most 9. 相似文献
13.
Let M be a hyperbolic manifold of finite volume which fibers over the circle with fiber a once punctured torus, and let S be an arbitrary incompressible surface in M. We determine the characteristic Jaco-Shalen-Johannson-submanifold of M−S and show, in particular, that Guts (M, S) is empty.
Received: 02 April 2004 相似文献
14.
Yoshinobu Kamishima 《Central European Journal of Mathematics》2014,12(6):861-878
We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type. 相似文献
15.
Anton A. Ayzenberg 《Proceedings of the Steklov Institute of Mathematics》2018,302(1):16-32
We consider an effective action of a compact (n ? 1)-torus on a smooth 2n-manifold with isolated fixed points. We prove that under certain conditions the orbit space is a closed topological manifold. In particular, this holds for certain torus actions with disconnected stabilizers. There is a filtration of the orbit manifold by orbit dimensions. The subset of orbits of dimensions less than n ? 1 has a specific topology, which is axiomatized in the notion of a sponge. In many cases the original manifold can be recovered from its orbit manifold, the sponge, and the weights of tangent representations at fixed points. We elaborate on the introduced notions using specific examples: the Grassmann manifold G4,2, the complete flag manifold F3, and quasitoric manifolds with an induced action of a subtorus of complexity 1. 相似文献
16.
The (4n+3)-dimensional sphere S4n+3 can be viewed as the boundary of the quaternionic hyperbolic space and the group PSp(n+1,1) of quaternionic hyperbolic isometries extends to a real analytic transitive action on S4n+3. We call the pair (PSp(n+1,1),S4n+3) a spherical Q C-C geometry. A manifold M locally modelled on this geometry is said to be a spherical Q C-C manifold. We shall classify all pairs (G,M) where G is a three-dimensional connected Lie group which acts smoothly and almost freely on a compact spherical Q C-C manifold M, preserving the geometric structure. As an application, we shall determine all compact 3-pseudo-Sasakian manifolds admitting spherical Q C-C structures. 相似文献
17.
Let X be a locally finite simplicial complex of dimension n, n? 5, equipped with a k-fold end structure [4] and consider a piecewise linear (n + 1)-dimensional manifold M that is proper homotopy equivalent to X × R by F:M → X × R, where R is the set of real numbers. The question arises as to whether or not the manifold M can be split, i.e., written as M = N × R where N is a n-manifold and where there is a proper homotopy between F and (p1 ° F0) × id:N × R → X × R, preserving the natural (k+1)-fold end structure, where F0 is F|N and p1 is the projection X × R → X. Of particular significance is the fact that X is noncompact. When the construction of such splittings is attempted, algebraic obstructions arise, which vanish if and only if the construction can be completed. This paper develops such an obstruction theory by utilizing methods of L.C. Siebenmann and the k-fold end structures of F. Waldhausen. 相似文献
18.
A set S⊆V is called a q+-set (q--set, respectively) if S has at least two vertices and, for every u∈S, there exists v∈S,v≠u such that N+(u)∩N+(v)≠∅ (N-(u)∩N-(v)≠∅, respectively). A digraph D is called s-quadrangular if, for every q+-set S, we have |∪{N+(u)∩N+(v):u≠v,u,v∈S}|?|S| and, for every q--set S, we have |∪{N-(u)∩N-(v):u,v∈S)}?|S|. We conjecture that every strong s-quadrangular digraph has a Hamilton cycle and provide some support for this conjecture. 相似文献
19.
A finite group action on a lens space L(p,q) has ‘type OR’ if it reverses orientation and has an invariant Heegaard torus whose sides are interchanged by the orientation-reversing elements. In this paper we enumerate the actions of type OR up to equivalence. This leads to a complete classification of geometric finite group actions on amphicheiral lens spaces L(p,q) with p>2. The family of actions of type OR is partially ordered by lifting actions via covering maps. We show that each connected component of this poset may be described in terms of a subset of the lattice of Gaussian integers ordered by divisibility. This results in a correspondence equating equivalence classes of actions of type OR with pairs of Gaussian integers. 相似文献
20.
Let Λ=|Se|/|Se+Sh|, where Sh and Se are independently distributed as Wishart distributions Wp(q,Σ) and Wp(n,Σ), respectively. Then Λ has Wilks’ lambda distribution Λp,q,n which appears as the distributions of various multivariate likelihood ratio tests. This paper is concerned with theoretical accuracy for asymptotic expansions of the distribution of T=-nlogΛ. We derive error bounds for the approximations. It is necessary to underline that our error bounds are given in explicit and computable forms. 相似文献