# Stick number of tangles

Youngsik Huh, Jung Hoon Lee, Kouki Taniyama

## 抄録

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.

本文言語 English 1750094 Journal of Knot Theory and its Ramifications 26 13 https://doi.org/10.1142/S0218216517500948 Published - 2017 11 1

• 代数と数論

## フィンガープリント

「Stick number of tangles」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。