共查询到20条相似文献,搜索用时 125 毫秒
1.
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
2.
Paul Norbury 《Geometriae Dedicata》2008,134(1):153-176
We give an identity involving sums of functions of lengths of simple closed geodesics, known as a McShane identity, on any
non-orientable hyperbolic surface with boundary which generalises Mirzakhani’s identities on orientable hyperbolic surfaces
with boundary.
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3.
Toru Ikeda 《Geometriae Dedicata》2014,170(1):177-183
The aims of this paper is to prove that every closed connected orientable 3-manifold with an orientation-preserving periodic diffeomorphism contains infinitely many, setwise invariant, spatial graphs whose exteriors are hyperbolic 3-manifolds. 相似文献
4.
Richard Brown 《Geometriae Dedicata》2003,97(1):129-150
In this note, we show that given a closed, orientable genus-g surface S
g
, any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S
g
. To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism. 相似文献
5.
The first examples of totally geodesic Seifert surfaces are constructed for hyperbolic knots and links, including both free
and totally knotted surfaces. Then it is proved that two bridge knot complements cannot contain totally geodesic orientable
surfaces. 相似文献
6.
For every closed orientable hyperbolic Haken 3-manifold and, more generally, for any orientable hyperbolic 3-manifold M which is homeomorphic to the interior of a Haken manifold, the number 0.286 is a Margulis number. If H 1(M;ℚ) ≠ 0, or if M is closed and contains a semi-fiber, then 0.292 is a Margulis number for M. 相似文献
7.
D. Blanusa 《Annali di Matematica Pura ed Applicata》1962,57(1):321-337
Summary C∞ — isometric imbeddings of the hyperbolic plane and of the two types of orientable cylinders with hyperbolic metric in spherical8-space are constructed, furthermore C∞ — isometric imbeddings of the non-orientable cylinder with hyperbolic metric in Euclidean8-space and in spherical10-space.
To Enrico Bompiani on his scientific Jubilee. 相似文献
8.
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
9.
T. Soma 《Commentarii Mathematici Helvetici》1997,72(4):582-592
Let be a closed, orientable surface of genus > 1. In this paper, non-trivial elements of the third bounded cohomology with are given constructively by using both a hyperbolic metric and a singular euclidean metric on . Furthermore, it is shown that the dimension of the subspace of consisting of zero-norm elements is the cardinality of the continuum.
Received: November 26, 1996 相似文献
10.
We prove that every three-dimensional maximal globally hyperbolic spacetime, locally modelled on the anti-de Sitter space
AdS
3, with closed orientable Cauchy surfaces, admits a unique CMC time function. 相似文献
11.
12.
A. Yu. Vesnin 《Mathematical Notes》1998,64(1):15-19
In 1931 F. Löbell constructed the first example of a closed orientable three-dimensional hyperbolic manifold. In the present paper we study properties of closed hyperbolic 3-manifolds generalizing Löbell's classical example. Explicit formulas for the volumes of these manifolds in terms of the Lobachevski function are obtained.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 17–23, July, 1998.This research was partially supported by GARC-KOSEF (Global Analysis Research Center of National Seoul University) and by the Russian Foundation for Basic Research under grant No. 95-01-01410. 相似文献
13.
In this note, we extend the Bridgeman–Kahn identity to all finite-volume orientable hyperbolic n-manifolds with totally geodesic boundary. In the compact case, Bridgeman and Kahn are able to express the manifold’s volume as the sum of a function over only the orthospectrum. For manifolds with non-compact boundary, our extension adds terms corresponding to intrinsic invariants of boundary cusps. 相似文献
14.
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
15.
Qiang Zhang 《数学学报(英文版)》2015,31(5):797-810
Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold B M,and fπ : π1(M) →π1(M) be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rank Fix(fπ) 2rankπ1(M),which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups. 相似文献
16.
João M. Nogueira 《Israel Journal of Mathematics》2018,225(2):909-924
We show the existence of infinitely many knots where each exterior contains meridional essential surfaces of independently unbounded genus and number of boundary components. In particular, we construct examples of knot exteriors each of which has all possible compact orientable surfaces embedded as meridional essential surfaces. From these results, we also prove the existence of a hyperbolic knot exterior, not necessarily of a knot in the 3-sphere, for which there are meridional essential surfaces of simultaneously unbounded genus and number of boundary components. 相似文献
17.
T. M. Mitryakova O. V. Pochinka 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):194-215
We consider diffeomorphisms of orientable surfaces with the nonwandering set consisting of a finite number of hyperbolic fixed
points and the wandering set containing a finite number of heteroclinic orbits of transversal and nontransversal intersection.
We distinguish a meaningful class of diffeomorphisms and present a complete topological invariant for this class. The invariant
is a scheme consisting of a set of numerical parameters and a set of geometric objects. 相似文献
18.
Alexander Stoimenow 《Combinatorica》2016,36(5):557-589
We prove that a planar cubic cyclically 4-connected graph of odd χ < 0 is the dual of a 1-vertex triangulation of a closed orientable surface. We explain how this result is related to (and applied to prove at a separate place) a theorem about hyperbolic volume of links: the maximal volume of alternating links of given χ < 0 does not depend on the number of their components. 相似文献
19.
《Expositiones Mathematicae》2021,39(3):384-410
We review basic facts on the structure of nearly Kähler manifolds, focussing in particular on the six-dimensional case. A self-contained proof that nearly Kähler six-manifolds are Einstein is given by combining different known results. We finally rephrase the definition of nearly Kähler six-manifold in terms of a pair of partial differential equations. 相似文献
20.
We consider orientable hyperbolic 3‐manifolds with either non‐empty compact geodesic boundary, or some toric cusps, or both. For any such M we analyze what portion of the volume of M can be recovered by inserting in M boundary collars and cusp neighbourhoods with disjoint embedded interiors. Our main result is that this portion can only be maximal in some combinatorially extremal configurations. The techniques we employ are very elementary but the result is in our opinion of some interest. 相似文献