# crossing change

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## Mathematics Subject Classification

### Weird knot universe

> when is a "crossing over" not a "crossing under"?

Does anyone know of some weird, exotic, theoretical universe in which a crossing over in a knot can also be a crossing under?

### Re: Weird knot universe

Does anyone know of some weird, exotic, theoretical universe in which a crossing over in a knot can also be a crossing under?

Our own universe. Sorry if that sounds like a smart-aleck response. For example, a kid who ties his shoes with double knots, or even triple knots. Then some crossings over will also be crossings under.

### Re: Weird knot universe

> Our own universe. Sorry if that sounds like a smart-aleck response. For example, a kid who ties his shoes with double knots, or even triple knots. Then some crossings over will also be crossings under.

So then are you saying the answer is: when each crossing involves only two subsections of the knot?

### Re: Weird knot universe

That would satisfy me, but I'm no super-literalist and I don't care much for theoretical universes (outside the context of sci-fi).