scholarly journals Hyperbolic manifolds with geodesic boundary which are determined by their fundamental group

2004 ◽  
Vol 145 (1-3) ◽  
pp. 69-81 ◽  
Author(s):  
Roberto Frigerio
Keyword(s):  
Fundamental Group ◽  
Hyperbolic Manifolds ◽  
Geodesic Boundary

scholarly journals The simplicial volume of hyperbolic manifolds with geodesic boundary

2010 ◽  
Vol 10 (2) ◽  
pp. 979-1001 ◽  
Author(s):  
Roberto Frigerio ◽  
Cristina Pagliantini
Keyword(s):  
Hyperbolic Manifolds ◽  
Geodesic Boundary ◽  
Simplicial Volume

scholarly journals Volumes of hyperbolic manifolds with geodesic boundary

Topology ◽  
1994 ◽  
Vol 33 (4) ◽  
pp. 613-629 ◽  
Author(s):  
Yosuke Miyamoto
Keyword(s):  
Hyperbolic Manifolds ◽  
Geodesic Boundary

Chains that realize the Gromov invariant of hyperbolic manifolds

1997 ◽  
Vol 17 (3) ◽  
pp. 643-648 ◽  
Author(s):  
DOUGLAS JUNGREIS
Keyword(s):  
Hyperbolic Manifold ◽  
Homology Class ◽  
Hyperbolic Manifolds ◽  
Uniform Measure ◽  
Geodesic Boundary ◽  
Maximal Volume ◽  
Totally Geodesic ◽  
Gromov Norm

For any closed hyperbolic manifold of dimension $n \geq 3$, suppose a sequence of $n$-cycles representing the fundamental homology class have norms converging to the Gromov invariant. We show that this sequence must converge to the uniform measure on the space of maximal-volume ideal simplices. As a corollary, we show that for a hyperbolic $n$-manifold $L$ ($n \geq 3$) with totally-geodesic boundary, the Gromov norm of ($L,\partial L$) is strictly greater than the volume of $L$ divided by the maximal volume of an ideal $n$-simplex.

scholarly journals Ruelle Zeta Functions of Hyperbolic Manifolds and Reidemeister Torsion

2021 ◽  
Author(s):  
Werner Müller
Keyword(s):  
Fundamental Group ◽  
General Result ◽  
Hyperbolic Manifold ◽  
Zeta Functions ◽  
Hyperbolic Manifolds ◽  
Reidemeister Torsion ◽  
Finite Dimensional ◽  
Orthogonal Representations ◽  
Ruelle Zeta Function ◽  
Complex Valued

AbstractThis paper is concerned with the behavior of twisted Ruelle zeta functions of compact hyperbolic manifolds at the origin. Fried proved that for an orthogonal acyclic representation of the fundamental group of a compact hyperbolic manifold, the twisted Ruelle zeta function is holomorphic at $$s=0$$ s = 0 and its value at $$s=0$$ s = 0 equals the Reidemeister torsion. He also established a more general result for orthogonal representations, which are not acyclic. The purpose of the present paper is to extend Fried’s result to arbitrary finite dimensional representations of the fundamental group. The Reidemeister torsion is replaced by the complex-valued combinatorial torsion introduced by Cappell and Miller.

scholarly journals Hyperbolic groups with boundary an n-dimensional Sierpinski space

2019 ◽  
Vol 11 (01) ◽  
pp. 233-247
Author(s):  
Jean-François Lafont ◽  
Bena Tshishiku
Keyword(s):  
Fundamental Group ◽  
Negative Curvature ◽  
Hyperbolic Group ◽  
Hyperbolic Groups ◽  
Manifolds With Boundary ◽  
Geodesic Boundary ◽  
Totally Geodesic ◽  
Visual Boundary ◽  
Aspherical Manifolds ◽  
Torsion Free

For [Formula: see text], we show that if [Formula: see text] is a torsion-free hyperbolic group whose visual boundary [Formula: see text] is an [Formula: see text]-dimensional Sierpinski space, then [Formula: see text] for some aspherical [Formula: see text]-manifold [Formula: see text] with non-empty boundary. Concerning the converse, we construct, for each [Formula: see text], examples of aspherical manifolds with boundary, whose fundamental group [Formula: see text] is hyperbolic, but with visual boundary [Formula: see text] not homeomorphic to [Formula: see text]. Our examples even support (metric) negative curvature, and have totally geodesic boundary.

scholarly journals A Menagerie of SU(2)-Cyclic 3-Manifolds

2021 ◽  
Author(s):  
Steven Sivek ◽  
Raphael Zentner
Keyword(s):  
Fundamental Group ◽  
Lens Space ◽  
Hyperbolic Manifolds ◽  
Cyclic Surgery ◽  
Dehn Fillings

Abstract We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image, respectively, among geometric 3-manifolds that are not hyperbolic. As an application, we give examples of hyperbolic 3-manifolds that do not admit degree-1 maps to any Seifert Fibered manifold other than $S^3$ or a lens space. We also produce infinitely many one-cusped hyperbolic manifolds with at least four $SU(2)$-cyclic Dehn fillings, one more than the number of cyclic fillings allowed by the cyclic surgery theorem.

scholarly journals Local rigidity of hyperbolic manifolds with geodesic boundary

2012 ◽  
Vol 5 (4) ◽  
pp. 757-784
Author(s):  
Steven P. Kerckhoff ◽  
Peter A. Storm
Keyword(s):  
Hyperbolic Manifolds ◽  
Geodesic Boundary ◽  
Local Rigidity

scholarly journals Truncated tetrahedra and their reflection groups

1998 ◽  
Vol 64 (1) ◽  
pp. 54-72 ◽  
Author(s):  
T. H. Marshall
Keyword(s):  
Hyperbolic Space ◽  
Hyperbolic Manifolds ◽  
Dihedral Angles ◽  
Manifolds With Boundary ◽  
Reflection Groups ◽  
Geodesic Boundary ◽  
Totally Geodesic ◽  
Generating Sets ◽  
Free Subgroups ◽  
Torsion Free

AbstractWe outline the classification, up to isometry, of all tetrahedra in hyperbolic space with one or more vertices truncated, for which the dihedral angles along the edges formed by the truncations are all π/2, and those remaining are all submultiples of π. We show how to find the volumes of these polyhedra, and find presentations and small generating sets for the orientation-preserving subgroups of their reflection groups.For particular families of these groups, we find low index torsion free subgroups, and construct associated manifolds and manifolds with boundary. In particular, for each g ≥ 2, we find a sequence of hyperbolic manifolds with totally geodesic boundary of genus g, which we conjecture to be of least volume among such manifolds.

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