arXiv math/98060801998-06math.MGmath.GT

A knotted minimal tree

Krystyna Kuperberg

备注：: 14 pages, 14 figures, to appear in Communications in Contemporary Mathematics

英文摘要：

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?''

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