BraidIsKnot

Whether a braid's closure is a knot rather than a multi-component link — its underlying permutation is a single cycle.

BraidIsKnot(braid)whether the closure has exactly one component

Typed signatures

Type	Package	Applies
`(expression<Braid> \| string) -> boolean`	`braid`	always

Domain: Braids and knots

Examples

Basic #

$\sigma_1^3$ has a single-cycle permutation

\mathrm{BraidIsKnot}(\mathrm{Braid}(2, \bigl\lbrack1, 1, 1\bigr\rbrack))

Out

\mathrm{True}

$\sigma_1^2$ closes to two components

\mathrm{BraidIsKnot}(\mathrm{Braid}(2, \bigl\lbrack1, 1\bigr\rbrack))

Out

\mathrm{False}

About

Examples	2