共查询到20条相似文献,搜索用时 9 毫秒
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Masakazu Teragaito 《Topology and its Applications》2009,156(6):1148-1152
For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic manifolds. Such exceptional surgeries are classified into four types, lens space surgery, small Seifert fibered surgery, toroidal surgery and reducing surgery, according to the resulting manifolds. For each of the three types except reducing surgery, we give infinitely many hyperbolic knots with integral exceptional Dehn surgeries of the given type, whose adjacent integral surgeries are not exceptional. 相似文献
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The problem of classifying, up to isometry, the orientable 3-manifolds that arise by identifying the faces of a Platonic solid was completely solved in a nice paper of Everitt [B. Everitt, 3-manifolds from Platonic solids, Topology Appl. 138 (2004) 253-263]. His work completes the classification begun by Best [L.A. Best, On torsion-free discrete subgroups of PSL2(C) with compact orbit space, Canad. J. Math. 23 (1971) 451-460], Lorimer [P.J. Lorimer, Four dodecahedral spaces, Pacific J. Math. 156 (2) (1992) 329-335], Prok [I. Prok, Classification of dodecahedral space forms, Beiträge Algebra Geom. 39 (2) (1998) 497-515], and Richardson and Rubinstein [J. Richardson, J.H. Rubinstein, Hyperbolic manifolds from a regular polyhedron, Preprint]. In this paper we investigate the topology of closed orientable 3-manifolds from Platonic solids. Here we completely recognize those manifolds in the spherical and Euclidean cases, and state topological properties for many of them in the hyperbolic case. The proofs of the latter will appear in a forthcoming paper. 相似文献
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The problem of classifying, up to isometry, the orientable 3-manifolds that arise by identifying the faces of a Platonic solid was completely solved in a nice paper of Everitt [B. Everitt, 3-manifolds from Platonic solids, Topology Appl. 138 (2004) 253-263]. His work completes the classification begun by Best [L.A. Best, On torsion-free discrete subgroups of PSL2(C) with compact orbit space, Canad. J. Math. 23 (1971) 451-460], Lorimer [P.J. Lorimer, Four dodecahedral spaces, Pacific J. Math. 156 (2) (1992) 329-335], Prok [I. Prok, Classification of dodecahedral space forms, Beiträge Algebra Geom. 39 (2) (1998) 497-515; I. Prok, Fundamental tilings with marked cubes in spaces of constant curvature, Acta Math. Hungar. 71 (1-2) (1996) 1-14], and Richardson and Rubinstein [J. Richardson, J.H. Rubinstein, Hyperbolic manifolds from a regular polyhedron, preprint]. In a previous paper we investigated the topology of closed orientable 3-manifolds from Platonic solids in the spherical and Euclidean cases, and completely classified them, up to homeomorphism. Here we describe many topological properties of closed hyperbolic 3-manifolds arising from Platonic solids. As a consequence of our geometric and topological methods, we improve the distinction between the hyperbolic “Platonic” manifolds with the same homology, which up to this point was only known by computational means. 相似文献
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Colin Adams 《Mathematische Annalen》1995,302(1):177-195
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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
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Paul Wedrich 《Journal of Pure and Applied Algebra》2019,223(4):1434-1439
We compute q-holonomic formulas for the HOMFLY polynomials of 2-bridge links colored with one-column (or one-row) Young diagrams. 相似文献
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Akio Kawauchi 《Geometriae Dedicata》1996,61(2):205-217
We construct a large class of finitely many hyperbolic homology 3-spheres making the following invariants equal, simultaneously, the integral homology, the quantum SU(2) invariants, the hyperbolic volume, the hyperbolic isometry group, the -invariant, the Chern-Simons invariant, and the Floer homology. 相似文献
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Toru Ikeda 《Topology and its Applications》2012,159(1):279-282
For any closed connected orientable 3-manifold M, we present a method for constructing infinitely many hyperbolic spatial embeddings of a given finite graph with no vertex of degree less than two from hyperbolic spatial graphs in S3 via the Heegaard splitting theory. These spatial embeddings are adjustable so as to take cycle subgraphs into specified homotopy classes of loops in M. 相似文献
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Ying-Qing Wu 《Mathematische Annalen》1996,304(1):457-480
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Hitoshi Murakami 《Advances in Mathematics》2007,211(2):678-683
We propose a version of the volume conjecture that would relate a certain limit of the colored Jones polynomials of a knot to the volume function defined by a representation of the fundamental group of the knot complement to the special linear group of degree two over complex numbers. We also confirm the conjecture for the figure-eight knot and torus knots. This version is different from S. Gukov's because of a choice of polarization. 相似文献
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Teruhisa Kadokami 《Topology and its Applications》2008,155(15):1699-1707
We introduce the norm and the order of a polynomial and of a homology lens space. We calculate the norm of the cyclotomic polynomials, and apply it to lens surgery problem for a knot whose Alexander polynomial is the same as an iterated torus knot. 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
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Jonathan A. Hillman 《Topology and its Applications》2011,158(3):468-478
We compute the p-primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free S1-action. Any linking pairing on a finite abelian group of odd order is realized by such a manifold. We find necessary and sufficient conditions for a pairing on an abelian 2-group to be the 2-primary component of such a linking pairing, and give simple examples which are not realizable by any Seifert fibred 3-manifold. 相似文献
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We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere. 相似文献
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Tsuyoshi Kobayashi 《Topology and its Applications》1985,20(1):67-78
In this paper we consider a non-singular Morse-Smale flow Φt on an irreducible, simple, closed, orientable 3-manifold M. We define a primitive flow ψt from Φt, and call the link type of the closed orbits of ψt a primitive link of Φt. We show that the link types of the primitive links are finite and every non-singular Morse-Smale flow on M is obtained from a primitive flow by exchanging the flow in a regular neighborhood of attracting or repelling closed orbits. 相似文献
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Every 1-connected topological 4-manifold M admits a S1-covering by # r − 1 S2 × S3, where
Received: 4 July 2004 相似文献