Results 41 to 50 of about 379,230 (325)
The Teichmuller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible [PDF]
, 2004 For a smooth manifold M we define the Teichmuller space 2T(M) of all Riemannian metrics on M and the Teichmuller space 2T€(M) of € -pinched negatively curved metrics on M, where 0 < € < oo. We prove that if M is hyperbolic, the natural inclusion ?f€(M)
T. Farrell, P. Ontaneda
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Finite groups and hyperbolic manifolds [PDF]
Inventiones mathematicae, 2005 The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg and Kojima, respectively.
Belolipetsky, M., Lubotzky, A.
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Proceedings of the American Mathematical Society, 1985 There is a regular 4 4 -dimensional polyhedron with 120 dodecahedra as 3 3 -dimensional faces. (Coxeter calls it the " 120 120 -cell".) The group of symmetries of this polyhedron is the Coxeter group with diagram: \[ [ u n k ] [unk] \] For each pair ...
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Topological invariants and Holomorphic Mappings
Comptes Rendus. Mathématique, 2022 Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are ...
Greene, Robert E. +2 more
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Symmetries of Hyperbolic 4-Manifolds [PDF]
International Mathematics Research Notices, 2015 In this paper, for each finite group $G$, we construct explicitly a non-compact complete finite-volume arithmetic hyperbolic $4$-manifold $M$ such that $\mathrm{Isom}\,M \cong G$, or $\mathrm{Isom}^{+}\,M \cong G$. In order to do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic $4$-space, on one hand, and the combinatorics of ...
Kolpakov, Alexander, SLAVICH, LEONE
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Infrared phases of 3D class R theories
Journal of High Energy Physics, 2022 We study the IR phases of 3D class R theories associated with closed non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional slopes.
Sunjin Choi, Dongmin Gang, Hee-Cheol Kim
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Partial Differential Equations and Quantum States in Curved Spacetimes
Mathematics, 2021 In this review paper, we discuss the relation between recent advances in the theory of partial differential equations and their applications to quantum field theory on curved spacetimes. In particular, we focus on hyperbolic propagators and the role they
Zhirayr Avetisyan, Matteo Capoferri
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Determinant of the Laplacian on a non-compact three-dimensional hyperbolic manifold with finite volume [PDF]
, 1996 The functional determinant of Laplace-type operators on a three-dimensional non-compact hyperbolic manifold with invariant fundamental domain of finite volume is expressed via the Selberg zeta function related to the Picard group .
A. Bytsenko, G. Cognola, S. Zerbini
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Volumes of hyperbolic manifolds [PDF]
Journal of Differential Geometry, 1983 The set of volumes of hyperbolic 3-manifolds is a closed well-ordered (nondiscrete) subset of \(\mathbb R^+\) [see \textit{W. Thurston}, ''The geometry and topology of three-manifolds'', mimeographed notes, Princeton Univ., Princeton 1980]. The main result of this paper is that the set of covolumes of discrete arithmetic irreducible subgroups of the ...
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Identities on hyperbolic manifolds [PDF]
, 2016 In this survey, we discuss four classes of identities due principally to Basmajian, McShane, Bridgeman-Kahn and Luo-Tan on hyperbolic manifolds and provide a unified approach for proving them. We also elucidate on the connections between the various identities.
Bridgeman, Martin, Tan, Ser Peow
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