Finite-volume Hyperbolic 3-Manifolds contain immersed Quasi-Fuchsian surfaces

Abstract

The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.

arXiv commentFinal version to appear in AGT. Some typos corrected, particularly def (3.6). Rewording of 4 paragraphs in proof of (4.2) for added clarity. Final section added comparing this paper to the approach of Masters and Zhang

References in corpus (5)

• Some surface subgroups survive surgery
• A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
• Closed Quasi-Fuchsian Surfaces In Hyperbolic Knot Complements
• Quasi-Fuchsian Surfaces In Hyperbolic Link Complements
• Conservative Subgroup Separability For Surfaces With Boundary

Cited by in corpus (7)

• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Nearly Fuchsian surface subgroups of finite covolume Kleinian groups
• Problems In Groups, Geometry, and Three-Manifolds
• Incompressible surfaces in rank one locally symmetric spaces
• Infinitely many virtual geometric triangulations
• Subgroups of Genus-2 Quasi-Fuchsian groups and Cocompact Kleinian Groups
• Closed Minimal Surfaces in Cusped Hyperbolic Three-manifolds