Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic $3$–manifolds
| Autor: | Daryl Cooper, David Futer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Fundamental group immersed surface Geodesic Covering space 20H10 Group Theory (math.GR) Disjoint sets 01 natural sciences 30F40 Mathematics - Geometric Topology Corollary 0103 physical sciences FOS: Mathematics 57M50 30F40 20H10 20F65 0101 mathematics 20F65 hyperbolic 3-manifold Mathematics Finite volume method 010102 general mathematics Hyperbolic 3-manifold Geometric Topology (math.GT) Mathematics::Geometric Topology quasifuchsian 57M50 010307 mathematical physics Geometry and Topology cubulation Cube Mathematics - Group Theory |
| Zdroj: | Geom. Topol. 23, no. 1 (2019), 241-298 |
| Popis: | This paper proves that every finite volume hyperbolic 3-manifold M contains a ubiquitous collection of closed, immersed, quasi-Fuchsian surfaces. These surfaces are ubiquitous in the sense that their preimages in the universal cover separate any pair of disjoint, non-asymptotic geodesic planes. The proof relies in a crucial way on the corresponding theorem of Kahn and Markovic for closed 3-manifolds. As a corollary of this result and a companion statement about surfaces with cusps, we recover Wise's theorem that the fundamental group of M acts freely and cocompactly on a CAT(0) cube complex. 34 pages, 2 figures. v2 contains added references and a strengthened statement of Corollary 1.3. v3 contains minor corrections and revisions, including a discussion of virtual specialness. This version will appear in Geometry & Topology |
| Databáze: | OpenAIRE |
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