A knotted minimal tree
Krystyna Kuperberg
Abstract
This paper contains a construction of a finite set X in the boundary of the unit 3-ball in R3 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 B3, let T be a tree in B3 of minimal length containing X. Is T unknotted, that is, is there a PL imbedded 2-ball in B3 containing T?''
Create a lesson
Related papers
Each simplex in R4 has a point with at least 14 emanating normals to its boundary
Ivan Nasonov, Gaiane Panina
Pointed Gromov-Hausdorff Distance between lp-Wedge Sums and Isometric Embeddings of l∞
Emin Abdullaev
Embedding large subsets of Wasserstein spaces into Banach spaces
Cyril Letrouit, Quentin Mérigot
A Smooth Covariogram and the Transition Between Projection Bodies
J. Haddad, C. H. Jiménez, M. Resende Guedes
Intermediate coverings, random images, and projections
Yunhao Zhao, Yingyu Zhao, Chen Zhou et al.
On the Graph Corresponding to Center of Distances of Metric Space
Oleksiy Dovgoshey, Olga Rovenska