## Knotscape

Knotscape is a software package developed by Morwen Thistletwaite and can be downloaded from his website (unix only). It is installed on our system here at the University of Utah mathematics department.

To start knotscape, log in and type

knotscape

A window with menus will appear. Click on browse->load. This loads a knot in the form of a sequence of numbers. The first number 8 means that there are 8 crossings. The second number 1 means that this is the first knot on a list of 8-crossing alternating knots. The remaining numbers describe the crossings themselves. This is called Dowker's notation and you can read about it in Adams' book. Now dismiss the green subwindow and click on action->draw knot so you can see what the knot you chose looks like. Then click on action->compute polynomials->Jones polynomial->compute. You get a new window with a sequence of numbers. The first two numbers you will recognize immediately. The next two numbers are -1 and 7 and they mean that the powers of the terms in the Jones polynomial go from -1 to 7 and the remaining numbers are the coefficients. Thus the Jones polynomial of the knot is

-t^{-1}-2+4t-5t^{2}+6t^{3}-5t^{4}+4t^{5}-3t^{6}+t^{7}

Another way to enter a knot is to draw it yourself via File->LinkSmith. You can use the middle mouse button to change crossings after you are done drawing a polygonal curve. Then click on file->submit and continue as before.

If you look around the menus, you will see that knotscape can do many other things with knots. You can read about them in Adams' book. There is also a tutorial under the help menu.