共查询到20条相似文献,搜索用时 33 毫秒
1.
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
2.
The Teichmüller TQFT, defined by Andersen and Kashaev, gives rise to a quantum invariant of triangulated hyperbolic knot complements; it has an associated volume conjecture, where the hyperbolic volume of the knot appears as a certain asymptotic coefficient.In this note, we announce a proof of this volume conjecture for all twist knots up to 14 crossings; along the way we explicitly compute the partition function of the Teichmüller TQFT for the whole infinite family of twist knots.Among other tools, we use an algorithm of Thurston to construct a convenient ideal triangulation of a twist knot complement, as well as the saddle point method for computing limits of complex integrals with parameters. 相似文献
3.
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
4.
A diagram D of a knot defines the corresponding Gauss Diagram G
D
. However, not all Gauss diagrams correspond to the ordinary knot diagrams. From a Gauss diagram G we construct closed surfaces F
G
and S
G
in two different ways, and we show that if the Gauss diagram corresponds to an ordinary knot diagram D, then their genus is the genus of the canonical Seifert surface associated to D. Using these constructions we introduce the virtual canonical genus invariant of a virtual knot and find estimates on the number of alternating knots of given genus and given crossing number. 相似文献
5.
Sebastian W. Hensel 《Geometriae Dedicata》2011,155(1):31-67
Let X be a closed hyperbolic surface and λ, η be weighted geodesic multicurves which are short on X. We show that the iterated grafting along λ and η is close in the Teichmüller metric to grafting along a single multicurve which can be given explicitly in terms of λ and
η. Using this result, we study the holonomy lifts gr
λ
ρ
X,λ of Teichmüller geodesics ρ
X,λ for integral laminations λ and show that all of them have bounded Teichmüller distance to the geodesic ρ
X,λ. We obtain analogous results for grafting rays. Finally we consider the asymptotic behaviour of iterated grafting sequences
gr
nλ
X and show that they converge geometrically to a punctured surface. 相似文献
6.
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
7.
We consider the weighted Bergman spaces
HL2(\mathbb Bd, ml){\mathcal {H}L^{2}(\mathbb {B}^{d}, \mu_{\lambda})}, where we set dml(z) = cl(1-|z|2)l dt(z){d\mu_{\lambda}(z) = c_{\lambda}(1-|z|^2)^{\lambda} d\tau(z)}, with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators
on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which
the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert–Schmidt operators on the generalized
Bergman spaces. 相似文献
8.
We introduce a two-variable polynomial invariant of a long virtual knot, which dominates the Kauffman f-polynomial and the Miyazawa polynomial of the closure. Our invariant satisfies a product formula for the concatenation product of long virtual knots. It describes a formula of the Miyazawa polynomial of a ‘connected sum’ of two virtual knots. It also gives lower bounds for the real crossing number and the virtual crossing number of a long virtual knot. 相似文献
9.
Shichao Chen 《The Ramanujan Journal》2009,18(1):103-112
Let Λ={λ
1≥⋅⋅⋅≥λ
s
≥1} be a partition of an integer n. Then the Ferrers-Young diagram of Λ is an array of nodes with λ
i
nodes in the ith row. Let λ
j
′ denote the number of nodes in column j in the Ferrers-Young diagram of Λ. The hook number of the (i,j) node in the Ferrers-Young diagram of Λ is denoted by H(i,j):=λ
i
+λ
j
′−i−j+1. A partition of n is called a t-core partition of n if none of the hook numbers is a multiple of t. The number of t-core partitions of n is denoted by a(t;n). In the present paper, some congruences and distribution properties of the number of 2
t
-core partitions of n are obtained. A simple convolution identity for t-cores is also given.
相似文献
10.
Greg Friedman 《Israel Journal of Mathematics》2008,163(1):139-188
We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots D
n−2 ↪ D
n
. Any two disk knots are cobordant if the cobordisms are not required to fix the boundary sphere knots, and any two even-dimensional
disk knots with isotopic boundary knots are cobordant rel boundary. However, the cobordism rel boundary theory of odd-dimensional
disk knots is more subtle. Generalizing results of J. Levine on the cobordism of sphere knots, we define disk knot Seifert
matrices and show that two higher-dimensional disk knots with isotopic boundaries are cobordant rel boundary if and only if
their disk knot Seifert matrices are algebraically cobordant. We also ask which algebraic cobordism classes can be realized
given a fixed boundary knot and provide a complete classification when the boundary knot has no 2-torsion in its middle-dimensional
Alexander module.
In the course of this classification, we establish a close connection between the Blanchfield pairing of a disk knot and the
Farber-Levine torsion pairing of its boundary knot (in fact, for disk knots satisfying certain connectivity assumptions, the
disk knot Blanchfield pairing will determine the boundary Farber-Levine pairing). In addition, we study the dependence of
disk knot Seifert matrices on choices of Seifert surface, demonstrating that all such Seifert matrices are rationally S-equivalent, but not necessarily integrally S-equivalent. 相似文献
11.
Darryn Bryant Melinda Buchanan Daniel Horsley Barbara Maenhaut Victor Scharaschkin 《Combinatorica》2011,31(5):507-528
We establish new lower bounds on the pair covering number C
λ
(υ,k) for infinitely many values of υ, k and λ, including infinitely many values of υ and k for λ=1. Here, C
λ
(υ,k) denotes the minimum number of k-subsets of a υ-set of points such that each pair of points occurs in at least λ of the k-subsets. We use these results to prove simple numerical conditions which are both necessary and sufficient for the existence
of (K
k
− e)-designs with more points than blocks. 相似文献
12.
13.
V. I. Burenkov M. Lanza de Cristoforis 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):68-89
We consider the Robin Laplacian in two bounded regions Ω1 and Ω2 of ℝ
N
with Lipschitz boundaries and such that Ω2 ⊂ Ω1, and we obtain two-sided estimates for the eigenvalues λ
n,2 of the Robin Laplacian in Ω2 via the eigenvalues λ
n, 1 of the Robin Laplacian in Ω1. Our estimates depend on the measure of the set difference Ω\Ω2 and on suitably defined characteristics of vicinity of the boundaries ∂Ω1 and ∂Ω2, and of the functions defined on ∂Ω1 and on ∂Ω2 that enter the Robin boundary conditions. 相似文献
14.
Most bounds for expected delay, E[D], in GI/GI/c queues are modifications of bounds for the GI/GI/1 case. In this paper we exploit a new delay recursion for the GI/GI/c queue to produce bounds of a different sort when the traffic intensity p = λ/μ = E[S]/E[T] is less than the integer portion of the number of servers divided by two. (S AND T denote generic service
and interarrival times, respectively.) We derive two different families of new bounds for expected delay, both in terms of
moments of S AND T. Our first bound is applicable when E[S2] < ∞. Our second bound for the first time does not require finite variance of S; it only involves terms of the form E[Sβ], where 1 < β < 2. We conclude by comparing our bounds to the best known bound of this type, as well as values obtained from
simulation.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
C. Adams A. Colestock J. Fowler W. Gillam E. Katerman 《Transactions of the American Mathematical Society》2006,358(2):727-741
Singular maps of surfaces into a hyperbolic 3-manifold are utilized to find upper bounds on meridian length, -curve length and maximal cusp volume for the manifold. This allows a proof of the fact that there exist hyperbolic knots with arbitrarily small cusp density and that every closed orientable 3-manifold contains a knot whose complement is hyperbolic with maximal cusp volume less than or equal to 9. We also find particular upper bounds on meridian length, -curve length and maximal cusp volume for hyperbolic knots in depending on crossing number. Particular improved bounds are obtained for alternating knots.
16.
Fumikazu Nagasato 《Topology and its Applications》2012,159(4):1059-1063
In this paper, applying Chebyshev polynomials we give a basic proof of the irreducibility over the complex number field of the defining polynomial of SL2(C)-character variety of twist knots in infinitely many cases. The irreducibility, combined with a result in the paper of M. Boileau, S. Boyer, A.W. Reid and S. Wang in 2010, shows the minimality of infinitely many twist knots for a partial order on the set of prime knots defined by using surjective group homomorphisms between knot groups. In Appendix B, we also give a straightforward proof of the result of Boileau et al. 相似文献
17.
Songliang Qiu 《中国科学A辑(英文版)》1998,41(12):1241-1247
Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation.
from which infinite-product representations of the Hersch-Pfluger ϕdimtortion function ϕ
K
(r) and the Agard η-distortion function η
K
(t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the
Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true. 相似文献
18.
Sergio Albeverio Zbignew Haba Francesco Russo 《Probability Theory and Related Fields》2001,121(3):319-366
A two-space dimensional heat equation perturbed by a white noise in a bounded volume is considered. The equation is perturbed
by a non-linearity of the type λ : f(AU) :, where :: means Wick (re)ordering with respect to the free solution;λ, A are small parameters, U denotes a solution, f is the Fourier transform of a complex measure with compact support.
Existence and uniqueness of the solution in a class of Colombeau-Oberguggenberger generalized functions is proven. An explicit
construction of the solution is given and it is shown that each term of the expansion in a power series in λ is associated
with an L
2-valued measure when A is a small enough.
Received: 20 July 1997 / Revised version: 1 February 2001 / Published online: 9 October 2001 相似文献
19.
We provide some more explicit formulae to facilitate the computation of Ohtsuki’s rational invariants λ
n
of integral homology 3-spheres extracted from Reshetikhin-TuraevSU(2) quantum invariants. Several interesting consequences will follow from our computation of λ2. One of them says that λ2 is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ1 is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained
from surgery on knots by using the Jones polynomial.
The first author is supported in part by NSF and the second author is supported by an NSF Postdoctoral Fellowship. 相似文献
20.
We obtain necessary conditions for a doubly triangular matrix A to have the property that a double series ΣΣ λ
mn
b
mn
is summable |A|
k
whenever the series ΣΣb
mn
is bounded |A|
k
. 相似文献