orourke@whatever.cs.jhu.edu (Joseph O'Rourke) (03/20/91)
Has anyone implemented a program that searches for a sequence of Reidemeister moves to convert one knot into another, or one knot into the unknot? Any references would be appreciated. Thanks!
arshad@cs.ed.ac.uk (Arshad Mahmood) (03/23/91)
In article <10453@cs.jhu.edu> orourke%sophia@cs.umass.edu (Joseph O'Rourke) writes: >Has anyone implemented a program that searches for a sequence >of Reidemeister moves to convert one knot into another, >or one knot into the unknot? Any references would be appreciated. I can think of no article specifically related to using Reidmeister moves, but an article by Thistlewaite in "Aspects of topology: in memory of Hugh Dowker 1912-1982" comes to mind. It discusses an algorithm for knot classification. It shouldn't be very difficult to implement such a program, since there are only 4 (I think !) moves to perform. There would naturally be a state-space explosion, but I suspect this is inevitable. You could cut the search space down quite a lot by using any of the well known polynomials, to see if the knots are equivalent at all. A good place to start for this is the paper by Louis Kauffman (it's in the AMS series, I don't have the exact reference at hand (shame on me!) if you don't know it then get in touch and I will send the proper reference.) I hope this is some help, best of luck ! Title: Aspects of topology: in memory of Hugh Dowker 1912-1982 London Mathematical Society Vol. 93 1985 A. Mahmood LFCS Edinburgh University Scotland