共查询到20条相似文献,搜索用时 15 毫秒
1.
Sue Goodman 《Topology and its Applications》2007,154(16):2962-2975
We consider C1 nonsingular flows on a closed 3-manifold under which there is no transverse disk that flows continuously back into its own interior. We provide an algorithm for modifying any branched surface transverse to such a flow ? that terminates in a branched surface carrying a foliation F precisely when F is transverse to ?. As a corollary, we find branched surfaces that do not carry foliations but that lift to ones that do. 相似文献
2.
We generalize Turaev's definition of torsion invariants of pairs (M,&\xi;), where M is a 3-dimensional manifold and &\xi; is an Euler structure on M (a non-singular vector field up to homotopy relative to ∂M and modifications supported in a ball contained in Int(M)). Namely, we allow M to have arbitrary boundary and &\xi; to have simple (convex and/or concave) tangency circles to the boundary. We prove that
Turaev's H
1(M)-equivariance formula holds also in our generalized context. Using branched standard spines to encode vector fields we show
how to explicitly invert Turaev's reconstruction map from combinatorial to smooth Euler structures, thus making the computation
of torsions a more effective one. Euler structures of the sort we consider naturally arise in the study of pseudo-Legendrian
knots (i.e.~knots transversal to a given vector field), and hence of Legendrian knots in contact 3-manifolds. We show that torsion, as
an absolute invariant, contains a lifting to pseudo-Legendrian knots of the classical Alexander invariant. We also precisely
analyze the information carried by torsion as a relative invariant of pseudo-Legendrian knots which are framed-isotopic.
Received: 3 October 2000 / Revised version: 20 April 2001 相似文献
3.
Burak Ozbagci 《Topology and its Applications》2007,154(4):908-916
We describe explicit horizontal open books on some Seifert fibered 3-manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams for some of these contact structures. 相似文献
4.
Sandra Shields 《Topology and its Applications》2006,153(18):3496-3510
We use branched surfaces to define an equivalence relation on C1 codimension one foliations of any closed orientable 3-manifold that are transverse to some fixed nonsingular flow. There is a discrete metric on the set of equivalence classes with the property that foliations that are sufficiently close (up to equivalence) share important topological properties. 相似文献
5.
Burak Ozbagci 《Topology and its Applications》2011,158(5):718-727
We review Giroux's contact handles and contact handle attachments in dimension three and show that a bypass attachment consists of a pair of contact 1 and 2-handles. As an application we describe explicit contact handle decompositions of infinitely many pairwise non-isotopic overtwisted 3-spheres. We also give an alternative proof of the fact that every compact contact 3-manifold (closed or with convex boundary) admits a contact handle decomposition, which is a result originally due to Giroux. 相似文献
6.
Using contact surgery and equivariant bordism theory, we prove the existence of contact structures on all 5-dimensional spin
manifolds with certain finite fundamental groups.
Received September 13, 1999 / Revised version September 13, 2000 / Published online April 12, 2001 相似文献
7.
Brendan Owens 《Advances in Mathematics》2008,217(5):2353-2376
8.
Monotonicity and uniqueness of traveling waves for a reaction-diffusion model with a quiescent stage
Ping-An Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2178-2189
This paper is concerned with the monotonicity and uniqueness of traveling waves for a reaction-diffusion model with quiescent stage. We first obtain the exponential decay rate of wave profiles, and then we show that any profile is strictly monotone by using the strong comparison principle. Furthermore, we prove the uniqueness (up to translation) of all traveling waves including even the waves with minimal speed. 相似文献
9.
Let a cyclic group $G$ act either on a number field $\mathbb L$
or on a $3$-manifold $M$. Let $s_{\mathbb L}$ be the number of
ramified primes in the extension $\mathbb L^G\subset \mathbb L$ and $s_M$ be the number
of components of the branching set of the branched covering
$M\to M/G$. In this paper, we prove several formulas relating
$s_{\mathbb L}$ and $s_M$ to the induced $G$-action on $Cl(\mathbb L)$ and
$H_1(M),$ respectively.
We observe that the formulas for $3$-manifolds and number fields are
almost identical, and therefore, they provide new evidence for
the correspondence between $3$-manifolds and number fields
postulated in arithmetic topology. 相似文献
10.
Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the
number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus.
This estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second
bounded cohomology to ordinary cohomology is not injective.
Oblatum 8-IX-2000 & 20-X-2000?Published online: 29 January 2001 相似文献
11.
V. Braungardt 《Topology》2005,44(3):641-659
We prove that for every natural number k there are simply connected topological four-manifolds which have at least k distinct smooth structures supporting Einstein metrics, and also have infinitely many distinct smooth structures not supporting Einstein metrics. Moreover, all these smooth structures become diffeomorphic to each other after connected sum with only one copy of the complex projective plane. We prove that manifolds with these properties cover a large geographical area. 相似文献
12.
Jongil Park 《Mathematische Zeitschrift》2002,240(2):405-421
In this paper we construct a family of simply connected spin non-complex symplectic 4-manifolds which cover all but finitely
many allowed lattice points () lying in the region . Furthermore, as a corollary, we prove that there exist infinitely many exotic smooth structures on for all n large enough.
Received: 29 August 2000 / in final form: 15 August 2001 / Published online: 28 February 2002 相似文献
13.
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
14.
We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex spin structure. Our main result states that two closed oriented three-manifolds endowed with a complex spin structure are undistinguishable by complex spin invariants of degree zero if, and only if, their associated quadratic functions are isomorphic. 相似文献
15.
We exhibit 18 surfaces that can be mapped generically into 3-space with a single triple-point. The family should be used as a source of examples and counter-examples. 相似文献
16.
Let G be a cyclic group of order 3, 5 or 7, and X=E(n) be the relatively minimal elliptic surface with rational base. In this paper, we prove that under certain conditions on n, there exists a locally linear G-action on X which is nonsmoothable with respect to infinitely many smooth structures on X. This extends the main result of [X. Liu, N. Nakamura, Pseudofree Z/3-actions on K3 surfaces, Proc. Amer. Math. Soc. 135 (3) (2007) 903-910]. 相似文献
17.
In their recent preprint, Baldwin, Ozsváth and Szabó defined a twisted version (with coefficients in a Novikov ring) of a spectral sequence, previously defined by Ozsváth and Szabó, from Khovanov homology to Heegaard–Floer homology of the branched double cover along a link. In their preprint, they give a combinatorial interpretation of the E3-term of their spectral sequence. The main purpose of the present paper is to prove directly that this E3-term is a link invariant. We also give some concrete examples of computation of the invariant. 相似文献
18.
Alexander V. Rezounenko 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1707-516
We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach space are proved. To get the well-posed initial value problem we restrict our study to a smaller metric space, construct the dynamical system and prove the existence of a compact global attractor. 相似文献
19.
Rosa Gini 《manuscripta mathematica》2001,104(1):49-69
Some properties of non-orientable 3-manifolds are shown. In particular, for a connected, non-orientable 3-manifold M, the group of cobordism clases of immersions of surfaces in M is isomorphic to a group structure on the set H
2(M,Z/2Z)×H
1(M,Z/2Z)×Z/2Z.
Received: 8 June 2000 / Revised version: 2 October 2000 相似文献
20.
Lenhard L. Ng 《Topology》2003,42(1):55-82
We establish tools to facilitate the computation and application of the Chekanov-Eliashberg differential graded algebra (DGA), a Legendrian-isotopy invariant of Legendrian knots and links in standard contact three space. More specifically, we reformulate the DGA in terms of front projections, and introduce the characteristic algebra, a new invariant derived from the DGA. We use our techniques to distinguish between several previously indistinguishable Legendrian knots and links. 相似文献