Immersing almost geodesic surfaces in a closed hyperbolic three manifold

2012/04/09 by Jeremy Kahn, Vladimir Marković · 3 citations
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Advanced Combinatorial Mathematics #Mathematics #Embedding #Hyperbolic manifold #3-manifold #Manifold (fluid mechanics) #Pure mathematics #Geodesic #Closed manifold #Construct (python library) #Mathematical analysis #Invariant manifold #Hyperbolic function

paper · pdf · doi:10.4007/annals.2012.175.3.4

openalex publication_date 2012/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/18

Abstract

Let M 3 be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into M 3 so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.

Cited by

• Hierarchically hyperbolic spaces, I: Curve complexes for cubical groups
• Homology of curves and surfaces in closed hyperbolic 3-manifolds
• 3-manifold [wikipedia]

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