Three Dimensions of Knot Coloring

Carter, J. Scott; Silver, Daniel S.; Williams, Susan G.

doi:10.4169/amer.math.monthly.121.06.506

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Dehn Coloring2

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2023

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Cited by 11 publications

(2 citation statements)

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“…A Dehn p-coloring is trivial if every white region is labeled by There exists a classical invariant similar to the Dehn coloring, which is called the Fox coloring. Carter, Silver, and Williams [9] proved that these colorabilities are equivalent.…”

Section: Dehn Coloringmentioning

confidence: 98%

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The $p$-colorable subgroup of Thompson's group

Kodama¹,

Takano²

2023

Preprint

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Recently, Jones introduced a method of constructing knots and links from elements of Thompson's group F by using its unitary representations. He also defined several subgroups of F as the stabilizer subgroups and some researchers studied them algebraically. One of the subgroups is called the 3-colorable subgroup F, and the authors proved that all knots and links obtained from non-trivial elements of F are 3-colorable. In this paper, for any odd integer p greater than two, we define the p-colorable subgroup of F whose non-trivial elements yield p-colorable knots and links and show it is isomorphic to the certain Brown-Thompson group.

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Section: Dehn Coloringmentioning

confidence: 98%

“…In this section, we briefly review a link invariant obtained from a coloring of regions. See [9,20] for details. Let p ≥ 3 be an integer and D be a diagram of a link L.…”

Section: Dehn Coloringmentioning

confidence: 99%