Finite-volume hyperbolic 3-manifolds contain immersed quasi-fuchsian surfaces

DOI10.2140/agt.2015.15.1199zbMath1405.57027arXiv1408.4691OpenAlexW2951118776MaRDI QIDQ2346737

Mark D. Baker, Daryl Cooper

Publication date: 3 June 2015

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.4691

zbMATH Keywords

hyperbolic 3-manifoldquasi-Fuchsian surface

Mathematics Subject Classification ID

Geometric group theory (20F65) General geometric structures on low-dimensional manifolds (57M50) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (5)

Infinitely many virtual geometric triangulations ⋮ Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds ⋮ Geodesic flow of nonstrictly convex Hilbert geometries ⋮ Nearly Fuchsian surface subgroups of finite covolume Kleinian groups ⋮ Incompressible surfaces in rank one locally symmetric spaces

Cites Work

• Immersing almost geodesic surfaces in a closed hyperbolic three manifold
• Varieties of group representations and splittings of 3-manifolds
• Bounded, separating, incompressible surfaces in knot manifolds
• Closed quasi-Fuchsian surfaces in hyperbolic knot complements
• Function groups in Kleinian groups
• Die Untergruppen der freien Produkte von beliebigen Gruppen
• Some surface subgroups survive surgery
• Intersections of topologically tame subgroups of Kleinian groups
• Conservative subgroup separability for surfaces with boundary
• Geometrical finiteness for hyperbolic groups
• A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3-manifolds
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Essential closed surfaces in bounded 3-manifolds

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