Concepedia

Universal Bounds for Genus One Seifert Surfaces for Hyperbolic Knots and Surgeries with Non-Trivial JSJT-Decompositions

Yukihiro Tsutsumi

Interdisciplinary Information Sciences · 2003 · 17 citations · 6 references

Open access

Concepts

Discrete GeometryUniversal BoundsGeometryKnot TheoryNon-haken ManifoldsEnumerative GeometryNon-trivial Jsjt-decompositionsUniversal BoundComplex GeometryHyperbolic Knots

Abstract

A universal bound on the number of mutually disjoint non-parallel genus one Seifert surfaces for hyperbolic knots in non-Haken manifolds is given.

References

6

Simple knots in compact, orientable 3-manifolds

Robert C. Myers · Transactions of the American Mathematical Society · 1982 · 69 citations · Full text

Excellent 1-manifolds in compact 3-manifolds

Robert C. Myers · Topology and its Applications · 1993 · 65 citations · Full text

Geometry, Manifold Modeling, Global Analysis +2

Simple knots without unique minimal surfaces

Herbert C. Lyon · Proceedings of the American Mathematical Society · 1974 · 25 citations

Geometry, Simple Knots, Knot Theory +4

Simple Knots in Compact, Orientable 3-Manifolds

Robert C. Myers · Transactions of the American Mathematical Society · 1982 · 24 citations

Manifold Modeling, Topological Invariant, Knot Theory +1

The Canonical Decompositions of Some Family of Compact Orientable Hyperbolic 3-Manifolds with Totally Geodesic Boundary

Akira Ushijima · Geometriae Dedicata · 1999 · 21 citations