共查询到20条相似文献,搜索用时 15 毫秒
1.
Leonid Plachta 《Topology and its Applications》2007,154(15):2880-2887
Recently Stoimenow showed that for every knot K and any n∈N and u0?u(K) there is a prime knot Kn,uo which is n-equivalent to the knot K and has unknotting number u(Kn,uo) equal to u0. The similar result has been obtained for the 4-ball genus gs of a knot. Stoimenow also proved that any admissible value of the Tristram-Levine signature σξ can be realized by a knot with the given Vassiliev invariants of bounded order. In this paper, we show that for every knot K with genus g(K) and any n∈N and m?g(K) there exists a prime knot L which is n-equivalent to K and has genus g(L) equal to m. 相似文献
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Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parameterized by the positive integers), namely the cyclic branched coverings of the knot. In this paper, we give a formula for the Casson-Walker invariants of these 3-manifolds in terms of residues of a rational function (which measures the 2-loop part of the Kontsevich integral of a knot) and the signature function of the knot. Our main result actually computes the LMO invariant of cyclic branched covers in terms of a rational invariant of the knot and its signature function. 相似文献
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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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Yuya Koda 《Topology and its Applications》2009,156(3):577-593
In the present paper we give a formula for colored Turaev-Viro invariants of twist knots using special polyhedra derived from (1,1)-decomposition of the knots. 相似文献
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Naoko Kamada 《Topology and its Applications》2012,159(4):999-1006
Bourgoin defined the notion of a twisted link which corresponds to a stable equivalence class of links in oriented thickenings. It is a generalization of a virtual link. Some invariants of virtual links are extended for twisted links including the knot group and the Jones polynomial. In this paper, we generalize a multivariable polynomial invariant of a virtual link to a twisted link. We also introduce a quandle of a twisted link. 相似文献
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Dedicated to Professor G. Nöbeling on his eightyfifth birthday 相似文献
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For the distance of (1,1)-splittings of a knot in a closed orientable 3-manifold, it is an important problem whether a (1,1)-knot can admit (1,1)-splittings of different distances. In this paper, we give one-parameter families of hyperbolic (1,1)-knots such that each (1,1)-knot admits a Dehn surgery yielding the 3-sphere. It is remarkable that such knots are the first concrete examples each of whose (1,1)-splittings is of distance three. 相似文献
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Luis G. Valdez-Sánchez 《Topology and its Applications》2007,154(3):584-603
Let M be a compact, connected, orientable, irreducible 3-manifold and T0 an incompressible torus boundary component of M such that the pair (M,T0) is not cabled. By a result of C. Gordon, if (S,∂S),(T,∂T)⊂(M,T0) are incompressible punctured tori with boundary slopes at distance Δ=Δ(∂S,∂T), then Δ?8, and the cases where Δ=6,7,8 are very few and classified. We give a simplified proof of this result (or rather, of its reduction process), using an improved estimate for the maximum possible number of mutually parallel negative edges in the graphs of intersection of S and T. We also extend Gordon's result by allowing either S or T to be an essential Klein bottle. 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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Yuichi Kabaya 《Topology and its Applications》2007,154(14):2656-2671
Let M be an oriented hyperbolic 3-manifold with finite volume. In [W.D. Neumann, J. Yang, Bloch invariants of hyperbolic 3-manifolds, Duke Math. J. 96 (1999) 29-59. [9]], Neumann and Yang defined an element β(M) of Bloch group B(C) for M. For this β(M), volume and Chern-Simons invariant of M is represented by a transcendental function. In this paper, we define β(M,ρ,C,o)∈P(C) for an oriented 3-manifold M with boundary, a representation of its fundamental group , a pants decomposition C of ∂M and an orientation o on simple closed curves of C. Unlike in the case of finite volume, we construct an element of pre-Bloch group P(C), and we need essentially the pants decomposition on the boundary. The volume makes sense for β(M,ρ,C,o) and we can describe the variation of volume on the deformation space. 相似文献
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Simon A. King 《Topology and its Applications》2007,154(6):1141-1156
Turaev-Viro invariants are defined via state sum polynomials associated to a special spine or a triangulation of a compact 3-manifold. By evaluation of the state sum at any solution of the so-called Biedenharn-Elliott equations, one obtains a homeomorphism invariant of the manifold (“numerical Turaev-Viro invariant”). The Biedenharn-Elliott equations define a polynomial ideal. The key observation of this paper is that the coset of the state sum polynomial with respect to that ideal is a homeomorphism invariant of the manifold (“ideal Turaev-Viro invariant”), stronger than the numerical Turaev-Viro invariants. Using computer algebra, we obtain computational results on several examples of ideal Turaev-Viro invariants, for all closed orientable irreducible manifolds of complexity at most 9. 相似文献
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Mihai Halic 《Mathematische Zeitschrift》2006,252(1):157-208
We present a purely algebraic approach to the Hamiltonian / Gauge theoretical invariants associated to torus actions on affine
spaces. Secondly, we address the issue of computing the invariants: a localization and a genus recursion formula are deduced.
Partially supported by: EAGER - European Algebraic Geometry Research Training Network, contract No. HPRN-CT-2000-00099 (BBW). 相似文献
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Lorena Armas-Sanabria 《Topology and its Applications》2009,156(6):1037-1053
We are interested in knowing what type of manifolds are obtained by doing Dehn surgery on closed pure 3-braids in S3. In particular, we want to determine when we get S3 by surgery on such a link. We consider links which are small closed pure 3-braids; these are the closure of 3-braids of the form , where σ1, σ2 are the generators of the 3-braid group and e1, f1, e are integers. We study Dehn surgeries on these links, and determine exactly which ones admit an integral surgery producing the 3-sphere. This is equivalent to determining the surgeries of some type on a certain six component link L that produce S3. The link L is strongly invertible and its exterior double branch covers a certain configuration of arcs and spheres, which we call the hexatangle. Our problem is equivalent to determine which fillings of the spheres by integral tangles produce the trivial knot, which is what we explicitly solve. This hexatangle is a generalization of the pentangle, which is studied in [C.McA. Gordon, J. Luecke, Non-integral toroidal Dehn surgeries, Comm. Anal. Geom. 12 (2004) 417-485]. 相似文献
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The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property; namely it is a universal Vassiliev invariant of knots. We introduce a second grading of the Kontsevich integral, the Euler degree, and a geometric null-move on the set of knots. We explain the relation of the null-move to S-equivalence, and the relation to the Euler grading of the Kontsevich integral. The null-move leads in a natural way to the introduction of trivalent graphs with beads, and to a conjecture on a rational version of the Kontsevich integral, formulated by the second author and proven in Geom. Top 8 (2004) 115 (see also Kricker, preprint 2000, math/GT.0005284). 相似文献
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It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of
a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system.
We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix
associated to a chord diagram, and another in terms of counting paths of intersecting chords.
Electronic supplementary material to this article is available at and is accessible to authorized users.
* S. G. was partially supported by an NSF and by an Israel-US BSF grant.
† M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education. 相似文献
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A. Bruguières 《Journal of Pure and Applied Algebra》2006,204(1):170-194
A tortile (or ribbon) category defines invariants of ribbon (framed) links and tangles. We observe that these invariants, when restricted to links, string links, and more general tangles which we call turbans, do not actually depend on the braiding of the tortile category. Besides duality, the only pertinent data for such tangles are the double braiding and twist. We introduce the general notions of twine, which is meant to play the rôle of the double braiding (in the absence of a braiding), and the corresponding notion of twist. We show that the category of (ribbon) pure braids is the free category with a twine (a twist). We show that a category with duals and a self-dual twist defines invariants of stringlinks. We introduce the notion of turban category, so that the category of turban tangles is the free turban category. Lastly we give a few examples and a tannaka dictionary for twines and twists. 相似文献