共查询到20条相似文献,搜索用时 0 毫秒
1.
It is shown that every properly embedded incompressible surface in a handlebody can be constructed by a canonical gluing process. A simple condition is given which asserts that the result of the gluing process is an incompressible surface. A new notion of isotopy is introduced in order to distinguish surfaces belonging to distinct isotopy classes. Several examples (known and new) are constructed. 相似文献
2.
We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two handlebody. In the orientable case the embedding can be either separating or non-separating. We also consider the case in which the genus two handlebody is replaced by an orientable 3-manifold with a compressible boundary component of genus greater than or equal to two. 相似文献
3.
Ying-Qing Wu 《Topology》2004,43(2):319-342
It is known that an embedded essential surface F in a hyperbolic manifold M remains essential in Dehn filling spaces M(γ) for most slopes γ on a torus boundary component T of M. The main theorem of this paper is to generalize this result to immersed surfaces. More explicitly, if an immersed essential surface F has coannular slopes β1,…,βn on T, then there is a constant K such that F remains essential in M(γ) when Δ(γ,βi)>K for all i. It will also be shown that all but finitely many Freedman tubings of a geometrically finite surface in M are π1-injective. 相似文献
4.
Anna Donati 《Aequationes Mathematicae》1987,33(1):194-207
A family of 4-dimensional pseudomanifolds is introduced using a standard graph-theoretical representation of lens spaces Some homeomorphisms between these lens-like spaces are established, the computation of their fundamental groups and of bounds for their genera are carried out 相似文献
5.
Anna Donati 《Aequationes Mathematicae》1987,33(2-3):194-207
A family of 4-dimensional pseudomanifolds is introduced using a standard graph-theoretical representation of lens spaces Some homeomorphisms between these lens-like spaces are established, the computation of their fundamental groups and of bounds for their genera are carried out 相似文献
6.
In a very general setting, we show that a 3-manifold obtained as the orbit space of the basin of a topological attractor is either S2×S1 or irreducible.We then study in more detail the topology of a class of 3-manifolds which are also orbit spaces and arise as invariants of gradient-like diffeomorphisms (in dimension 3). Up to a finite number of exceptions, which we explicitly describe, all these manifolds are Haken and, by changing the diffeomorphism by a finite power, all the Seifert components of the Jaco-Shalen-Johannson decomposition of these manifolds are made into product circle bundles. 相似文献
7.
In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf spaces in general. 相似文献
8.
We show that if F is a smooth, closed, orientable surface embedded in a closed, orientable 3-manifold M such that for each Riemannian metric g on M, F is isotopic to a least-area surface F(g), then F is incompressible. 相似文献
9.
We say a knot k in the 3-sphere S3 has PropertyIE if the infinite cyclic cover of the knot exterior embeds into S3. Clearly all fibred knots have Property IE.There are infinitely many non-fibred knots with Property IE and infinitely many non-fibred knots without property IE. Both kinds of examples are established here for the first time. Indeed we show that if a genus 1 non-fibred knot has Property IE, then its Alexander polynomial Δk(t) must be either 1 or 2t2−5t+2, and we give two infinite families of non-fibred genus 1 knots with Property IE and having Δk(t)=1 and 2t2−5t+2 respectively.Hence among genus 1 non-fibred knots, no alternating knot has Property IE, and there is only one knot with Property IE up to ten crossings.We also give an obstruction to embedding infinite cyclic covers of a compact 3-manifold into any compact 3-manifold. 相似文献
10.
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
11.
We construct a crystallization of the real projective space whose associated contracted complex is minimal with respect to the number of n-simplexes. Then we compute the regular genus of , which is the minimum genus of a closed connected surface into which a crystallization of regularly embeds.
Received: 7 February 2007 相似文献
12.
Jesús González 《Topology》2003,42(4):907-927
Let α(d) denote the number of ones in the binary expansion of d. For 1?k?α(d) we prove that the 2(d+α(d)−k)+1-dimensional, 2k-torsion lens space does not immerse in a Euclidian space of dimension 4d−2α(d) provided certain technical condition holds. The extra hypothesis is easily eliminated in the case k=1 recovering Davis’ strong non-immersion theorem for real projective spaces. For k>1 this is a deeper problem (solved only in part) that requires a close analysis of the interaction between the Brown-Peterson 2-series and its 2k analogue. The methods are based on a partial generalization of the Brown-Peterson version for the Conner-Floyd conjecture used in this context to detect obstructions for the existence of Euclidian immersions. 相似文献
13.
14.
Every non-orientable 3-manifold M can be expressed as a union of three orientable handlebodies V
1,V
2,V
3 whose interiors are pairwise disjoint. If g
i
denotes the genus of ∂V
i and g
3≤g
2≤g
3, then the tri-genus of M is the minimum triple (g
1,g
2,g
3), ordered lexicographically. If the Bockstein of the first Stiefel–Whitney class βw
1(M)=0, then M has tri-genus (0,2g,g
3), where g is the minimal genus of a 2-sided Stiefel Whitney surface of M. In this paper it is shown that, if βw
1(M)&\ne;0, then M has tri-genus
(1,2g−1,g
3), where g is the minimal genus of a (1-sided) Stiefel–Whitney surface. As an application the tri-genus of certain graph manifolds is
computed.
Received: 28 April 1999 相似文献
15.
Jonathan Ariel Barmak 《Advances in Mathematics》2008,218(1):87-104
We present a new approach to simple homotopy theory of polyhedra using finite topological spaces. We define the concept of collapse of a finite space and prove that this new notion corresponds exactly to the concept of a simplicial collapse. More precisely, we show that a collapse X↘Y of finite spaces induces a simplicial collapse K(X)↘K(Y) of their associated simplicial complexes. Moreover, a simplicial collapse K↘L induces a collapse X(K)↘X(L) of the associated finite spaces. This establishes a one-to-one correspondence between simple homotopy types of finite simplicial complexes and simple equivalence classes of finite spaces. We also prove a similar result for maps: We give a complete characterization of the class of maps between finite spaces which induce simple homotopy equivalences between the associated polyhedra. This class describes all maps coming from simple homotopy equivalences at the level of complexes. The advantage of this theory is that the elementary move of finite spaces is much simpler than the elementary move of simplicial complexes: It consists of removing (or adding) just a single point of the space. 相似文献
16.
17.
Charalampos CharitosIoannis Papadoperakis Georgios Tsapogas 《Topology and its Applications》2011,158(8):978-995
A complex of incompressible surfaces in a handlebody is constructed so that it contains, as a subcomplex, the complex of curves of the boundary of the handlebody. For genus 2 handlebodies, the group of automorphisms of this complex is used to characterize the mapping class group of the handlebody. In particular, it is shown that all automorphisms of the complex of incompressible surfaces are geometric, that is, induced by a homeomorphism of the handlebody. 相似文献
18.
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.
David M. Austin 《Mathematische Annalen》1995,302(1):295-322
This work was partially supported by a grant from the National Sciences and Engineering Research Council 相似文献