From: lrudolph@panix.com (Lee Rudolph)
Subject: Re: How to identify the unknot?
Date: 27 Aug 2000 19:26:30 -0400
Newsgroups: sci.math
Summary: [missing]

domnei@aol.comXYZXYZ (Mike Keith) writes:

>I have a series of N points in 3-space: (x1,y1,z1), (x2,y2,z2)...(xN,yN,zN).
>Imagine a line drawn from point 1 to 2, then continuing (in a different
>direction,
>in general) to point 3 then 4...then N, and then back to 1, forming a closed
>loop.
>
>Can some one direct me to an algorithm (hopefully computer-programmable)
>that I can use to tell, given a set of values for the (xi,yi,zi), if the result
>is 
>equivalent to the unknot (or, conversely, if it is a knot)?  
>It's o.k. to assume the points are such that the curve does not 
>intersect itself.
>
>Thanks for any pointers or ideas.  I don't even know if this is a hard or
>easy problem, so just knowing that would be useful.

The state of the art for this problem is probably the paper
http://front.math.ucdavis.edu/math.GT/9801126 by Birman and Hirsch.
As to whether their algorithm (or any of the other known algorithms)
is "hopefully computer-programmable"...well, that depends, among 
other things, on how hopeful you are.  (How large is N likely to
be for you?)

Lee Rudolph