A knotted minimal tree
Metric Geometry
2007-05-23 v3 Geometric Topology
Abstract
This paper contains a construction of a finite set X in the boundary of the unit 3-ball in R^3 whose minimal tree is knotted. The example answers Problem 5.17 in ''Problems in Low-dimensional Topology'' by Rob Kirby posed by Michael Freedman: ''Given a finite set of points X in the boundary of B^3, let T be a tree in B^3 of minimal length containing X. Is T unknotted, that is, is there a PL imbedded 2-ball in B^3 containing T?''
Keywords
Cite
@article{arxiv.math/9806080,
title = {A knotted minimal tree},
author = {Krystyna Kuperberg},
journal= {arXiv preprint arXiv:math/9806080},
year = {2007}
}
Comments
14 pages, 14 figures, to appear in Communications in Contemporary Mathematics