John Conway has died

Re:John Conway has died by adeledeweylopez on Saturday April 11, 2020 @03:26PM (#22843572)

As a teen, I was obsessed with knot theory, and Conway's knot notation always felt like magic to me.

The notation works by counting the number of twists in a segment, and then looking for another twist directly connected to the previous twist, and so on.

This gives you a sequence of integers, one counting the number (and direction) of twists.

If the entire knot is made of twists connected this way, then the continued fraction you get from the sequence of numbers is a knot invariant!

https://www.maths.ed.ac.uk/~v1ranick/papers/conway.pdf

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Re:John Conway has died by whatshisface on Saturday April 11, 2020 @03:43PM (#22843694)

Can two different knots have the same integer sequence?

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Re:John Conway has died by kmill on Saturday April 11, 2020 @04:09PM (#22843853)

No, they can't, since they are just representations of the knot diagram.

As for uniqueness, even "rational knots," the ones from the simplest of the fundamental polyhedra, have multiple fractions representing them.

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Re:John Conway has died by sdenton4 on Saturday April 11, 2020 @03:54PM (#22843773)

I'm knot familiar with this one in particular, but a 'unique' knot invariant would be a very big deal. (It would then be a knot identifier...)

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Re:John Conway has died by saagarjha on Saturday April 11, 2020 @04:09PM (#22843855)

;)

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