Totally geodesic surfaces in hyperbolic 3-manifolds

DOI10.1017/S0013091500005010zbMath0714.57010OpenAlexW1953631362MaRDI QIDQ3200255

Alan W. Reid

Publication date: 1991

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500005010

zbMATH Keywords

totally geodesicfundamental group of a 3-manifoldarithmetic Kleinian groupssubgroups of PSL(2,C)hyperbolic 3-manifolds of finite volumeArithmetic 3-manifoldsChern-Simons invariant of an arithmetic Kleinian groupcocompact Fuchsian subgroupshyperbolic knot complementsproper incompressible immersion of a 2-manifold

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Fundamental group, presentations, free differential calculus (57M05) Embeddings in differential topology (57R40)

Related Items (11)

Finiteness of maximal geodesic submanifolds in hyperbolic hybrids ⋮ Quotients of Coxeter complexes, fundamental groupoids and regular graphs ⋮ Totally geodesic surfaces in twist knot complements ⋮ Geodesic planes in hyperbolic 3-manifolds ⋮ Rigidity, lattices, and invariant measures beyond homogeneous dynamics ⋮ Geodesic surfaces in the complement of knots with small crossing number ⋮ Geodesic Surfaces in Knot Complements ⋮ Arithmeticity, superrigidity, and totally geodesic submanifolds ⋮ Compressing totally geodesic surfaces ⋮ Small curvature laminations in hyperbolic 3-manifolds ⋮ Arithmeticity of hyperbolic -manifolds containing infinitely many totally geodesic surfaces

Cites Work

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• On the cuspidal cohomology of arithmetic subgroups of SL(2n) and the first Betti number of arithmetic 3-manifolds
• Thrice-Punctured Spheres in Hyperbolic 3-Manifolds
• Immersions and Embeddings of Totally Geodesic Surfaces
• A Small Arithmetic Hyperbolic Three-Manifold
• Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups
• Some Amalgam Structures for Bianchi Groups
• KNOTS WITH THE PARABOLIC PROPERTY P
• A quadratic parabolic group
• The structure of certain subgroups of the Picard group
• On a Theorem of Ahlfors and Conjugate Subgroups of Kleinian Groups
• Parabolic Representations of Knot Groups, I

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