A Note on Finite Dehn Fillings

AbstractLet M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in H1(∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.

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KÄHLER MANIFOLDS AND FUNDAMENTAL GROUPS OF NEGATIVELY δ-PINCHED MANIFOLDS

International Journal of Mathematics ◽

10.1142/s0129167x04002247 ◽

2004 ◽

Vol 15 (02) ◽

pp. 151-167

Author(s):

JÜRGEN JOST ◽

YI-HU YANG

Keyword(s):

Fundamental Group ◽

Finite Volume ◽

Kähler Manifold ◽

Hyperbolic Metric ◽

Fundamental Groups ◽

Kahler Manifolds ◽

Smooth Structure ◽

Kahler Manifold ◽

Topological Manifolds ◽

Compact Kähler Manifold

In this note, we will show that the fundamental group of any negatively δ-pinched [Formula: see text] manifold cannot be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in F4(-20) cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernández [3]. Finally, we follow Gromov and Thurston [6] to give some examples of negatively δ-pinched manifolds [Formula: see text] of finite volume which, as topological manifolds, admit no hyperbolic metric with finite volume under any smooth structure. This shows that our result for δ-pinched manifolds is a nontrivial generalization of the fact that no nonuniform lattice in SO(n,1)(n≥3) is the fundamental group of a quasi-compact Kähler manifold [21].

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TOPOLOGICAL PROPERTIES OF CYCLICALLY PRESENTED GROUPS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s021821650300241x ◽

2003 ◽

Vol 12 (02) ◽

pp. 243-268 ◽

Cited By ~ 19

Author(s):

ALBERTO CAVICCHIOLI ◽

DUŠAN REPOVŠ ◽

FULVIA SPAGGIARI

Keyword(s):

Finite Volume ◽

High Dimensional ◽

Fundamental Groups ◽

Topological Properties ◽

3 Dimensional ◽

Hnn Extensions ◽

Finite Set ◽

Split Extensions

We introduce a family of cyclic presentations of groups depending on a finite set of integers. This family contains many classes of cyclic presentations of groups, previously considered by several authors. We prove that, under certain conditions on the parameters, the groups defined by our presentations cannot be fundamental groups of closed connected hyperbolic 3–dimensional orbifolds (in particular, manifolds) of finite volume. We also study the split extensions and the natural HNN extensions of these groups, and determine conditions on the parameters for which they are groups of 3–orbifolds and high–dimensional knots, respectively.

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Integrality of volumes of representations

Mathematische Annalen ◽

10.1007/s00208-020-02047-9 ◽

2021 ◽

Author(s):

Michelle Bucher ◽

Marc Burger ◽

Alessandra Iozzi

Keyword(s):

Finite Volume ◽

Hyperbolic Manifolds ◽

3 Dimensional ◽

Definition Of ◽

Dehn Fillings

AbstractLet M be an oriented complete hyperbolic n-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [3] we show that the volume of a representation $$\rho :\pi _1(M)\rightarrow \mathrm {Isom}^+({{\mathbb {H}}}^n)$$ ρ : π 1 ( M ) → Isom + ( H n ) , properly normalized, takes integer values if n is even and $$\ge 4$$ ≥ 4 . If M is not compact and 3-dimensional, it is known that the volume is not locally constant. In this case we give explicit examples of representations with volume as arbitrary as the volume of hyperbolic manifolds obtained from M via Dehn fillings.

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On the fundamental groups of negatively curved manifolds with finite volume

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1979-0529223-7 ◽

1979 ◽

Vol 75 (1) ◽

pp. 99-99

Author(s):

Midori S. Goto

Keyword(s):

Finite Volume ◽

Fundamental Groups ◽

Curved Manifolds ◽

Negatively Curved

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Finite volume and spectral methods applied to Pb-30%TI alloy solidification

Journal de Physique IV (Proceedings) ◽

10.1051/jp4:2001618 ◽

2001 ◽

Vol 11 (PR6) ◽

pp. Pr6-151-Pr6-159 ◽

Cited By ~ 1

Author(s):

R. Guérin ◽

M. El Ganaoui ◽

P. Haldenwang ◽

P. Bontoux

Keyword(s):

Finite Volume ◽

Spectral Methods ◽

Ti Alloy ◽

Alloy Solidification

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New Finite Volume–Multiscale Finite-Element Model for Solving Solute Transport Problems in Porous Media

Journal of Hydrologic Engineering ◽

10.1061/(asce)he.1943-5584.0002044 ◽

2021 ◽

Vol 26 (3) ◽

pp. 04021002

Author(s):

Yifan Xie ◽

Zhenze Xie ◽

Jichun Wu ◽

Yong Chang ◽

Chunhong Xie ◽

...

Keyword(s):

Finite Element ◽

Porous Media ◽

Finite Element Model ◽

Solute Transport ◽

Finite Volume ◽

Element Model ◽

Multiscale Finite Element ◽

Transport Problems

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Filling words in fundamental groups of Riemann surfaces

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.50.2013.1.1227 ◽

2013 ◽

Vol 50 (1) ◽

pp. 31-50

Author(s):

C. Zhang

Keyword(s):

Riemann Surface ◽

Fundamental Group ◽

Riemann Surfaces ◽

Fundamental Groups ◽

Closed Geodesics ◽

New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

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