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7 votes

In knot theory, what is this link property and how to detect it: "linkings between components separate nicely"

Nice question--I'm not sure if this already has a name. Here is one way to show that a link is not a necklace, that applies to the Borromean rings. Suppose that the link has components $(R,G,B)$, and ...
2 votes

Are there infinite number of 3-braids with trivial closure?

Suppose that $\beta$ is a three-braid whose closure is trivial. Suppose that $\gamma$ is any three-braid. Then $\gamma \beta \gamma^{-1}$ is again a three-braid with trivial closure. However, if $\...
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1 vote

Space-time trajectory that cannot be straightened and its braid form

The answer to your second question is "no". Non-trivial braids can have braid closures yielding trivial knots (and links). As an example of this, consider the braid $\beta = \sigma_1 \...
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