A KNOTTED MINIMAL TREE

DOI10.1142/S0219199799000055zbMATH Open0958.57002arXivmath/9806080MaRDI QIDQ4514919

Krystyna Kuperberg

Publication date: 14 November 2000

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

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?

Full work available at URL: https://arxiv.org/abs/math/9806080

zbMATH Keywords

minimal treeknotted graph

Mathematics Subject Classification ID

Trees (05C05) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Relations of low-dimensional topology with graph theory (57M15)

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