SMALL CURVATURE SURFACES IN HYPERBOLIC 3-MANIFOLDS

DOI10.1142/S0218216506004531zbMath1090.57012arXivmath/0409455OpenAlexW2079692837MaRDI QIDQ5291353

Christopher J. Leininger

Publication date: 10 May 2006

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409455

zbMATH Keywords

totally geodesic surfaces in hyperbolic knot and link complements

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

Holonomy limits of complex projective structures ⋮ Totally geodesic surfaces and homology ⋮ Volumes of highly twisted knots and links ⋮ Embedding closed hyperbolic 3-manifolds in small volume hyperbolic 4-manifolds ⋮ Totally geodesic hyperbolic 3-manifolds in hyperbolic link complements of tori in \(S^4\) ⋮ A Birman-Series type result for geodesics with infinitely many self-intersections ⋮ Proving a manifold to be hyperbolic once it has been approximated to be so ⋮ Small curvature laminations in hyperbolic 3-manifolds

Cites Work

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• Closed incompressible surfaces in complements of star links
• The geometry of Teichmüller space via geodesic currents
• Almost alternating links
• Toroidally alternating knots and links
• Three-dimensional orbifolds and cone-manifolds
• Spherical space forms and Dehn filling
• On irreducible 3-manifolds which are sufficiently large
• Uniformization of small -orbifolds
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Dehn surgery on knots
• Complements of hyperbolic knots of braid index four contain no closed embedded totally geodesic surfaces

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