共查询到20条相似文献,搜索用时 15 毫秒
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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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Roberto Frigerio Carlo Petronio 《Transactions of the American Mathematical Society》2004,356(8):3243-3282
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and we discuss consistency and completeness equations. Moreover, building on previous work of Ushijima, we extend Weeks' tilt formula algorithm, which computes the Epstein-Penner canonical decomposition, to an algorithm that computes the Kojima decomposition.
Our theory has been exploited to classify all the orientable finite-volume hyperbolic -manifolds with non-empty compact geodesic boundary admitting an ideal triangulation with at most four tetrahedra. The theory is particularly interesting in the case of complete finite-volume manifolds with geodesic boundary in which the boundary is non-compact. We include this case using a suitable adjustment of the notion of ideal triangulation, and we show how this case arises within the theory of knots and links.
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Paola Bandieri 《Annali dell'Universita di Ferrara》1989,35(1):163-175
Summary In this paper we prove that the minimum among all regular genera of the graphs representing a 3-manifold with boundaryM
3 can always be obtained by a crystallization. As a consequence, we also prove that every 3-coloured graph representing ∂M
3 is the boundary of a 4-coloured graph which representsM
3 and whose genus equals the regular genus ofM
3.
Work performed under the auspices of the G.N.S.A.G.A.-C.N.R., and within the Project ?Geometria delle varietà differenziabili?, supported by M.P.I. of Italy. 相似文献
Riassunto In questo lavoro si prova che ogni 3-varietà con bordoM 3 ammette sempre una cristallizzazione di genere minimo. Come conseguenza, si ottiene che ogni grafo 3-colorato che rappresenta ∂M 3 è il bordo di un grafo 4-colorato che rappresentaM 3, il cui genere è uguale al genere regolare diM 3.
Work performed under the auspices of the G.N.S.A.G.A.-C.N.R., and within the Project ?Geometria delle varietà differenziabili?, supported by M.P.I. of Italy. 相似文献
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Makoto Tamura 《Transactions of the American Mathematical Society》1998,350(5):2129-2140
Feng Luo and Richard Stong introduced the average edge order of a triangulation and showed in particular that for closed 3-manifolds being less than 4.5 implies that is on . In this paper, we establish similar results for 3-manifolds with non-empty boundary; in particular it is shown that being less than 4 implies that is on the 3-ball.
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We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity.
We show that the same strategy can be applied in order to analyze simultaneously compact manifolds and finite-volume manifolds
with toric cusps. In contrast, we show that if one allows annular cusps, the number of manifolds grows very rapidly and our
strategy cannot be employed to obtain a complete list. We also carefully describe how to compute the volume of our manifolds,
discussing formulas for the volume of a tetrahedron with generic dihedral angles in hyperbolic space. 相似文献
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Cheikh Birahim Ndiaye 《Mathematische Zeitschrift》2011,269(1-2):83-114
Given a compact four-dimensional smooth Riemannian manifold (M,g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero. Using integral methods, we prove global existence and convergence for the Q-curvature flow to a smooth metric conformal to g of prescribed Q-curvature, zero T-curvature and vanishing mean curvature under conformally invariant assumptions. 相似文献
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We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two handlebody. In the orientable case the embedding can be either separating or non-separating. We also consider the case in which the genus two handlebody is replaced by an orientable 3-manifold with a compressible boundary component of genus greater than or equal to two. 相似文献
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Steven Boyer 《Commentarii Mathematici Helvetici》1993,68(1):20-47
Partially supported by NSERC grant A7819 and FCAR grant EQ3518. 相似文献
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Sangyop Lee 《Topology》2007,46(5):437-468
We estimate the number of exceptional slopes for hyperbolic 3-manifolds with a torus boundary component and at least one other boundary component. 相似文献
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I. Ishii 《Proceedings of the Steklov Institute of Mathematics》2006,252(1):74-84
A new complexity, called a block number, is defined for a combed 3-manifold, and a method for the combinatorial classification
of combed 3-manifolds with a given block number is proposed. 相似文献
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Amos Altshuler 《Journal of Combinatorial Theory, Series A》1974,16(2):165-173
It is proved that every combinatorial 3-manifold with at most eight vertices is a combinatorial sphere. 相似文献
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Hossein Abbaspour 《Comptes Rendus Mathematique》2004,338(9):713-718
Let M be a connected, closed, oriented and smooth manifold of dimension d. Let LM be the space of loops in M. Chas and Sullivan introduced the loop product, an associative product of degree ?d on the homology of LM. In this Note we aim at identifying 3-manifolds with “non-trivial” loop products. To cite this article: H. Abbaspour, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
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We give a simple surface interpretation for each summand in the evaluation of Turaev-Viro invariants, for the case of small
(up to eighth) roots of unity. From this interpretation follows an efficient scheme to compute these invariants. Extensive
tables relative to a rich variety of 3-manifolds are explicitly presented. 相似文献
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Joel Hass Shicheng Wang Qing Zhou 《Proceedings of the American Mathematical Society》2002,130(6):1851-1857
For any hyperbolic 3-manifold with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of is bounded from above.
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Thecalcualtionof〈zk1,zk2,…,zkn〉LofthispaperwillbeintermoftheKauffmanbracket-polynomial[1,2,3].TheKauffmanbracketpolynomialofaplanardiagramofanunorientedlinkisanelement〈D〉∈Z[A,A-1]definedbythefollowingprocess.AstateofDisdefinedtobeamapsfromthecrossing… 相似文献
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A complete classification is given for neighborly combinatorial 3-manifolds with 9 vertices. It is found that there are 51 types, only one of which is not a sphere. 相似文献