共查询到20条相似文献,搜索用时 15 毫秒
1.
BRUNO ZIMMERMANN 《Geometriae Dedicata》1997,66(2):149-157
It is well known that different knots or links in the 3-sphere can have homeomorphic n-fold cyclic branched coverings. We consider the following problem: for which values of nis a knot of link determined by itsn-fold cyclic branched covering? We consider the class of hyperbolic resp.2π/n-hyperbolic links. The isometry or symmetry groups of such links are finite, and their n-fold branched coverings are hyperbolic 3-manifolds. Our main result states that if ndoes not divide the order of the finite symmetry group of such a link, then the link is determined by its n-fold branched covering. In a sense, the result is best possible; the key argument of its proof is algebraic using some basic result about finite p-groups. The main result applies, for example, to the cyclic branched coverings of the 2-bridge links; in particular, it gives a classification of the maximally symmetricD6-manifolds which are exactly the 3-fold branched coverings of the 2-bridge links. 相似文献
2.
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
3.
Fulvia Spaggiari 《Discrete Mathematics》2005,300(1-3):163-179
We study a family of closed connected orientable 3-manifolds (which are examples of tetrahedron manifolds) obtained by pairwise identifications of the boundary faces of a standard tetrahedron. These manifolds generalize those considered in previous papers due to Grasselli, Piccarreta, Molnár and Sieradski. Then we completely describe our tetrahedron manifolds in terms of Seifert fibered spaces, and determine their Seifert invariants. Moreover, we obtain different representations of our manifolds as 2-fold coverings, and give examples of non-equivalent knots with the same tetrahedron manifold as 2-fold branched covering space. 相似文献
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Marco Reni 《Mathematische Annalen》2000,316(4):681-697
We consider the following problem from the Kirby's list (Problem 3.25): Let K be a knot in and M(K) its 2-fold branched covering space. Describe the equivalence class [K] of K in the set of knots under the equivalence relation if is homeomorphic to . It is known that there exist arbitrarily many different hyperbolic knots with the same 2-fold branched coverings, due to
mutation along Conway spheres. Thus the most basic class of knots to investigate are knots which do not admit Conway spheres.
In this paper we solve the above problem for knots which do not admit Conway spheres, in the following sense: we give upper
bounds for the number of knots in the equivalence class [K] of a knot K and we describe how the different knots in the equivalence class of K are related.
Received: 3 August 1998 / in final form: 17 June 1999 相似文献
7.
We study the topological structure and the homeomorphism problem for closed 3-manifolds M(n,k) obtained by pairwise identifications of faces in the boundary of certain polyhedral 3-balls. We prove that they are (n/d)-fold cyclic coverings of the 3-sphere branched over certain hyperbolic links of d+1 components, where d= (n/k). Then we study the closed 3-manifolds obtained by Dehn surgeries on the components of these links.
Received: 27 November 1998 / Accepted: 12 May 1999 相似文献
8.
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
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In this paper, we prove that for any positive even integer m, there exists a hyperbolic knot such that its longitudinal Dehn surgery yields a 3-manifold containing a unique separating, incompressible torus, which meets the core of the attached solid torus in m points minimally. 相似文献
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We obtain an explicit representation as Dunwoody manifolds of all cyclic branched coverings of torus knots of type (p,mp±1), with p > 1 and m > 0. 相似文献
11.
We use methods from gauge theory to compute the Seifert volumes of 3-manifolds. As applications, we are able to find the Seifert volumes of several hyperbolic manifolds obtained by surgery on 2-bridge knots. 相似文献
12.
L. Paoluzzi 《Commentarii Mathematici Helvetici》1999,74(3):467-475
We prove that, for any given , a -hyperbolic knot is determined by its 2-fold and n-fold cyclic branched coverings. We also prove that a -hyperbolic knot which is not determined by its m-fold and n-fold cyclic branched coverings, , must have genus .
Received: December 14, 1998. 相似文献
13.
Marc Lackenby 《Geometriae Dedicata》2010,147(1):191-206
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold
M, in terms of data from any surgery diagram for M. This has several consequences. We prove that a family of hyperbolic alternating link complements is expanding if and only
if they have bounded volume. We also provide examples of hyperbolic 3-manifolds which require ‘complicated’ surgery diagrams,
thereby proving that a recent theorem of Constantino and Thurston is sharp. Along the way, we find a new upper bound on the
bridge number of a knot that is not tangle composite, in terms of the twist number of any diagram of the knot. The proofs
rely on a theorem of Lipton and Tarjan on planar graphs, and also the relationship between many different notions of width
for knots and 3-manifolds. 相似文献
14.
Maria Rita Casali 《Discrete Mathematics》2007,307(6):704-714
In [M.R. Casali, Computing Matveev's complexity of non-orientable 3-manifolds via crystallization theory, Topology Appl. 144(1-3) (2004) 201-209], a graph-theoretical approach to Matveev's complexity computation is introduced, yielding the complete classification of closed non-orientable 3-manifolds up to complexity six. The present paper follows the same point-of view, making use of crystallization theory and related results (see [M. Ferri, Crystallisations of 2-fold branched coverings of S3, Proc. Amer. Math. Soc. 73 (1979) 271-276; M.R. Casali, Coloured knots and coloured graphs representing 3-fold simple coverings of S3, Discrete Math. 137 (1995) 87-98; M.R. Casali, From framed links to crystallizations of bounded 4-manifolds, J. Knot Theory Ramifications 9(4) (2000) 443-458]) in order to significantly improve existing estimations for complexity of both 2-fold and three-fold simple branched coverings (see [O.M. Davydov, The complexity of 2-fold branched coverings of a 3-sphere, Acta Appl. Math. 75 (2003) 51-54] and [O.M. Davydov, Estimating complexity of 3-manifolds as of branched coverings, talk-abstract, Second Russian-German Geometry Meeting dedicated to 90-anniversary of A.D.Alexandrov, Saint-Petersburg, Russia, June 2002]) and 3-manifolds seen as Dehn surgery (see [G. Amendola, An algorithm producing a standard spine of a 3-manifold presented by surgery along a link, Rend. Circ. Mat. Palermo 51 (2002) 179-198]). 相似文献
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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
17.
We address the question that if π1-surjective maps between closed aspherical 3-manifolds have the same rank on π1 they must be of non-zero degree. The positive answer is proved for Seifert manifolds, which is used in constructing the first
known example of minimal Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero
degree between 3-manifolds. Many examples are given.
Received September 16, 1999, Revised August 31, 2000, Accepted March 29, 2001. 相似文献
18.
Daniel Matignon 《Topology and its Applications》2010,157(12):1900-1925
This paper explicitly provides two exhaustive and infinite families of pairs (M,k), where M is a lens space and k is a non-hyperbolic knot in M, which produces a manifold homeomorphic to M, by a non-trivial Dehn surgery. Then, we observe the uniqueness of such knot in such lens space, the uniqueness of the slope, and that there is no preserving homeomorphism between the initial and the final M's. We obtain further that Seifert fibered knots, except for the axes, and satellite knots are determined by their complements in lens spaces. An easy application shows that non-hyperbolic knots are determined by their complement in atoroidal and irreducible Seifert fibered 3-manifolds. 相似文献
19.
We discuss some relations between the invariant originated in Fukumoto-Furuta and the Neumann-Siebenmann invariant for the Seifert rational homology 3-spheres. We give certain constraints on Seifert 3-manifolds to be obtained by surgery on knots in homology 3-spheres in terms of these invariants.Mathematics Subject Classification (2000): 57M27, 57N13, 57N10Dedicated to Professor Yukio Matsumoto for his 60th birthday 相似文献
20.
We exhibit strong constraints on the geometry and topology of a uniformly quasiconformally homogeneous hyperbolic manifold. In particular, if n3, a hyperbolic n-manifold is uniformly quasiconformally homogeneous if and only if it is a regular cover of a closed hyperbolic orbifold. Moreover, if n3, we show that there is a constant Kn>1 such that if M is a hyperbolic n-manifold, other than which is K–quasiconformally homogeneous, then KKn.Mathematics Subject Classification (2000): 30C60Research supported in part by NSF grant 070335 and 0305704.Research supported in part by NSF grant 0203698.Research supported in part by the NZ Marsden Fund and the Royal Society (NZ).Research supported in part by NSF grant 0305704. 相似文献