Some ideas

[roseman at dimension4.math.uiowa.edu (Dennis M. Roseman)]

Dear Dave:

I have a couple of ideas for linktool you might be interested in  
thinking about.

Here is one kind of thing it would be nice to do:  enter a knot with  
a mouse, get a nice picture of it (so far so good) but now I want to  
put that nice picture back in the edit widow and make some more  
modifications.  As it is, none of the outputs of the nicely displayed  
links can be put directly back into an edit window.  One would use  
the fineness of spline points to decide how many straight edges to  
use.

It would be nice to be able to enter several of these in the same  
edit window, as different strands then one could connect them up and  
make various tanglings.

One might like to iterate this process several times.

Another thing that I would find useful is a display that shows a  
given knot as a nicely drawn knotted arc which might begin and end  
somewhere on say some fixed line (an axzis, say).  Given a knot there  
are several such pictures one gets depending on how one "breaks the  
circle to get the arc".  This would be useful to me in constructing  
nice versions of knotted spheres.  


How about something that would make a nice picture of a given braid?

I had some other thoughts along these lines, but I'm running low on  
time at the moment.

Dennis Roseman, Department of Mathematics, 

University of Iowa, Iowa City, Iowa, USA (52242)
E-mail: roseman at dimension4.math.uiowa.edu, or 

        roseman at oak.math.uiowa.edu
Tel: Office ((555) 555-5555  Dept. ((555) 555-5555
Fax: ((555) 555-5555