1. Energy functionals of knots II
- Author
-
Jun O'Hara
- Subjects
Knot complement ,Energy ,Knot ,Mathematical analysis ,Fibered knot ,Möbius energy ,Torus ,Knot energy ,Mathematics::Geometric Topology ,Combinatorics ,Knot (unit) ,Knot invariant ,Geometry and Topology ,Minimizer ,Computer Science::Databases ,Mathematics ,Energy functional - Abstract
We study an energy functional of knots, e p j ( jp > 2), that is finite valued for embedded circles and takes +∞ for circles with double points. We show that for any b ϵ R there are finitely many solid tori T 1 ,…, T m such that any knot with e p j ⩽ b can be contained in some T i in a good manner. Then we can show the existence of a minimizer of e p j in each knot type.
- Published
- 1994