Comments on A Neighborhood of Infinity: Untangling with Continued Fractions: Part 0

Understood. My motivations for this encoding were ...

2008-08-11T11:54:00.000-07:00

Understood. My motivations for this encoding were similar. i wanted a sanity check that the encodings for representations of Hopf algebra elements and spin networks as processes made sense.

leithaus,

A bit of googling reveals you've ...

2008-08-11T11:32:00.000-07:00

leithaus,

A bit of googling reveals you've given some talks on knots and processes. Cool! Anyway, I'll be taking a slightly different tack.

Knotation is cool, encoding knots in \pi-calculus ...

2008-08-11T11:23:00.000-07:00

Knotation is cool, encoding knots in \pi-calculus is cooler ;-)

You can associate processes with crossings and wires.

It turns out you need buffering to make things work and you have a design choice to make wires or crossings buffer.

You can then write a function from the Dowker-Thistlethwaite code for a knot to the process that encodes it.

You can also encode Reidemeister moves as operations on processes (encoding knots).

It is straightforward to see that R1 and R2 result in processes that are weakly bisimilar to the processes they were applied to. It's considerably more subtle to see this for R3.

Javier,

You're right. But using the antitwi...

2008-08-10T09:23:00.000-07:00

Javier,

You're right. But using the antitwist is convenient because if we use only twist and rotate it takes 5 operations to replace antitwist. I wasn't really thinking in terms of a minimal set of operations, I was just thinking that we have a group so I might as well use generators and their inverses whenever I feel like it.

Why do you need the anti-twist? cannot you recover...

2008-08-10T03:48:00.000-07:00

Why do you need the anti-twist? cannot you recover it from twist and rotation alone?

It'd be cool if I had some smart image processi...

2008-08-09T19:54:00.000-07:00
It'd be cool if I had some smart image processing code to do this...

See http://processing.org/