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Any link has a diagram with only triangles and quadrilaterals

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abstract

A link diagram can be considered as a $4$-valent graph embedded in the $2$-sphere and divides the sphere into complementary regions. In this paper, we show that any link has a diagram with only triangles and quadrilaterals. This extends previous results shown by the authors and C. Adams.

fields

math.GT 1

years

2024 1

verdicts

CONDITIONAL 1

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Quasitoric representation of generalized braids

math.GT · 2024-11-27 · conditional · novelty 5.0

Every oriented normal generalized link is the closure of a quasitoric normal generalized braid, and the quasitoric braids form a subgroup.

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  • Quasitoric representation of generalized braids math.GT · 2024-11-27 · conditional · none · ref 25 · internal anchor

    Every oriented normal generalized link is the closure of a quasitoric normal generalized braid, and the quasitoric braids form a subgroup.