Stick number of tangles

Youngsik Huh, Jung Hoon Lee, Kouki Taniyama

Research output: Contribution to journalArticlepeer-review

Abstract

An n-string tangle is a pair (B,A) such that A is a disjoint union of properly embedded n arcs in a topological 3-ball B. And an n-string tangle is said to be trivial (or rational)a, if it is homeomorphic to (D × I,{x1,⋯,xn}× I) as a pair, where D is a 2-disk, I is the unit interval and each xi is a point in the interior of D. A stick tangle is a tangle each of whose arcs consists of finitely many line segments, called sticks. For an n-string stick tangle its stick-order is defined to be a nonincreasing sequence (s1,s2,⋯,sn) of natural numbers such that, under an ordering of the arcs of the tangle, each si denotes the number of sticks constituting the ith arc of the tangle. And a stick-order S is said to be trivial, if every stick tangle of the order S is trivial. In this paper, restricting the 3-ball B to be the standard 3-ball, we give the complete list of trivial stick-orders.

Original languageEnglish
Article number1750094
JournalJournal of Knot Theory and its Ramifications
Volume26
Issue number13
DOIs
Publication statusPublished - 2017 Nov 1

Keywords

  • Stick number
  • knot
  • tangle

ASJC Scopus subject areas

  • Algebra and Number Theory

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