The complement of the figure-eight knot geometrically bounds
| Autor: | Leone Slavich |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems knot complement General Mathematics MathematicsofComputing_GENERAL Figure-eight knot 01 natural sciences Mathematics - Geometric Topology Hyperbolic manifolds knot complement geodesically embedding manifold geodesically bounding manifold Mathematics - Metric Geometry geodesically bounding manifold Bounding overwatch FOS: Mathematics Hyperbolic manifolds Mathematics - Combinatorics Regular ideal 0101 mathematics ComputingMethodologies_COMPUTERGRAPHICS Mathematics Complement (set theory) Knot complement Finite volume method Applied Mathematics 010102 general mathematics Geometric Topology (math.GT) Metric Geometry (math.MG) 51M10 51M15 51M20 52B11 Mathematics::Geometric Topology geodesically embedding manifold 010101 applied mathematics Tetrahedron Combinatorics (math.CO) Mathematics::Differential Geometry Knot (mathematics) |
| Zdroj: | Proceedings of the American Mathematical Society. 145:1275-1285 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | We show that some hyperbolic 3-manifolds which are tessellated by copies of the regular ideal hyperbolic tetrahedron embed geodesically in a complete, finite volume, hyperbolic 4-manifold. This allows us to prove that the complement of the figure-eight knot geometrically bounds a complete, finite volume hyperbolic 4-manifold. This the first example of geometrically bounding hyperbolic knot complement and, amongst known examples of geometrically bounding manifolds, the one with the smallest volume. 9 pages, 4 figures, typos corrected, improved exposition of tetrahedral manifolds. Added Proposition 3.3, which gives necessary and sufficient conditions for M_T to be a manifold, and Remark 4.4, which shows that the figure-eight knot bounds a 4-manifold of minimal volume. Updated bibliography |
| Databáze: | OpenAIRE |
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