共查询到20条相似文献,搜索用时 0 毫秒
1.
《Topology and its Applications》2000,100(2-3):219-222
We prove that for exceptional Seifert manifolds all weakly reducible Heegaard splittings are reducible. This provides the missing case for the Main Theorem in (Moriah and Schultens, to appear). It follows that for all orientable Seifert fibered spaces which fiber over an orientable base space, irreducible Heegaard splittings are either horizontal or vertical. 相似文献
2.
Jennifer Schultens 《Topology and its Applications》1999,100(2-3)
We prove that for exceptional Seifert manifolds all weakly reducible Heegaard splittings are reducible. This provides the missing case for the Main Theorem in (Moriah and Schultens, to appear). It follows that for all orientable Seifert fibered spaces which fiber over an orientable base space, irreducible Heegaard splittings are either horizontal or vertical. 相似文献
3.
Teruhiko Soma 《Transactions of the American Mathematical Society》2006,358(9):4057-4070
We will present a new proof of the rigidity theorem for Seifert fibered spaces of infinite by Scott (1983) in the case when the base of the fibration is a hyperbolic triangle 2-orbifold. Our proof is based on arguments in the rigidity theorem for hyperbolic 3-manifolds by Gabai (1997).
4.
5.
Let V∪S W be a reducible Heegaard splitting of genus g = g(S)≥2.For a maximal prime connected sum decomposition of V∪S W,let q denote the number of the genus 1 Heegaard splittings of S2×S1 in the decomposition,and p the number of all other prime factors in the decomposition.The main result of the present paper is to describe the relation of p,q and dim(C V∩CW). 相似文献
6.
We call a pair (K,m) of a knot K in the 3-sphere S3 and an integer m a Seifert fibered surgery if m-surgery on K yields a Seifert fiber space. For most known Seifert fibered surgeries (K,m), K can be embedded in a genus 2 Heegaard surface of S3 in a primitive/Seifert position, the concept introduced by Dean as a natural extension of primitive/primitive position defined by Berge. Recently Guntel has given an infinite family of Seifert fibered surgeries each of which has distinct primitive/Seifert positions. In this paper we give yet other infinite families of Seifert fibered surgeries with distinct primitive/Seifert positions from a different point of view. 相似文献
7.
8.
9.
We give a necessary and sufficient condition for Heegaard splittings of knot exteriors to admit destabilizations. As an application, we show the following: let K1 and K2 be a pair of knots which is introduced by Morimoto as an example giving degeneration of tunnel number under connected sum. The Heegaard splitting of the exterior of K1#K2 derived from certain minimal unknotting tunnel systems of K1 and K2 is stabilized. 相似文献
10.
Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are known to have a unique minimal genus splitting. Here we demonstrate that an infinite class of hyperbolic knot exteriors, namely exteriors of certain “twisted torus knots” originally studied by Morimoto, Sakuma and Yokota, have a unique minimal genus Heegaard splitting of genus two. We also conjecture that these manifolds possess irreducible yet weakly reducible splittings of genus three. There are no known examples of such Heegaard splittings. 相似文献
11.
The infimal Heegaard gradient of a 3-manifold was defined andstudied by Marc Lackenby in an approach towards proving thewell-known virtually Haken conjecture. As instructive examples,Seifert fibered 3-manifolds are considered in this paper. Theauthor shows that a compact orientable Seifert fibered 3-manifoldhas zero infimal Heegaard gradient if and only if it virtuallyfibers over either the circle or a surface other than the 2-sphereor, equivalently, if it has infinite fundamental group. 2000Mathematics Subject Classification 57M10 (primary), 57N10, 57M50(secondary). 相似文献
12.
Hyam Rubinstein Martin Scharlemann 《Transactions of the American Mathematical Society》1998,350(2):689-715
In a recent paper we used Cerf theory to compare strongly irreducible Heegaard splittings of the same closed irreducible orientable 3-manifold. This captures all irreducible splittings of non-Haken 3-manifolds. One application is a solution to the stabilization problem for such splittings: If are the genera of two splittings, then there is a common stabilization of genus . Here we show how to obtain similar results even when the 3-manifold has boundary.
13.
Jiming Ma 《Topology and its Applications》2011,158(3):409-411
Fixed an oriented handlebody H=H+ with boundary F, let η(H+)=H− be the mirror image of H+ along F, so η(F) is the boundary of H−, for a map f:F→F, we have a 3-manifold by gluing H+ and H− along F with attaching map f, and denote it by Mf=H+∪f:F→FH−. In this note, we show that there are involutions f:F→F which are also reducible, such that Mf have arbitrarily high Heegaard distances. 相似文献
14.
15.
In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition. 相似文献
16.
Partially supported by NSF grant DMS-8701746 相似文献
17.
Tatiana Evans 《Topology and its Applications》2006,153(14):2631-2647
J. Hempel [J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (3) (2001) 631-657] used the curve complex associated to the Heegaard surface of a splitting of a 3-manifold to study its complexity. He introduced the distance of a Heegaard splitting as the distance between two subsets of the curve complex associated to the handlebodies. Inspired by a construction of T. Kobayashi [T. Kobayashi, Casson-Gordon's rectangle condition of Heegaard diagrams and incompressible tori in 3-manifolds, Osaka J. Math. 25 (3) (1988) 553-573], J. Hempel [J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (3) (2001) 631-657] proved the existence of arbitrarily high distance Heegaard splittings.In this work we explicitly define an infinite sequence of 3-manifolds {Mn} via their representative Heegaard diagrams by iterating a 2-fold Dehn twist operator. Using purely combinatorial techniques we are able to prove that the distance of the Heegaard splitting of Mn is at least n.Moreover, we show that π1(Mn) surjects onto π1(Mn−1). Hence, if we assume that M0 has nontrivial boundary then it follows that the first Betti number β1(Mn)>0 for all n?1. Therefore, the sequence {Mn} consists of Haken 3-manifolds for n?1 and hyperbolizable 3-manifolds for n?3. 相似文献
18.
Ryan Derby-Talbot 《Topology and its Applications》2007,154(9):1841-1853
Let T be a separating incompressible torus in a 3-manifold M. Assuming that a genus g Heegaard splitting VS∪W can be positioned nicely with respect to T (e.g., VS∪W is strongly irreducible), we obtain an upper bound on the number of stabi-lizations required for VS∪W to become isotopic to a Heegaard splitting which is an amalgamation along T. In particular, if T is a canonical torus in the JSJ decomposition of M, then the number of necessary stabilizations is at most 4g−4. As a corollary, this establishes an upper bound on the number of stabilizations required for VS∪W and any Heegaard splitting obtained by a Dehn twist of VS∪W along T to become isotopic. 相似文献
19.
Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained and the allowable configurations are simple and useful. Splitting surfaces not conforming to these simple local pictures must be weakly reducible. 相似文献