Searching for ribbon disks for alternating knots ad hoc
The walkthrough below illustrates how to have KLO execute the ribbon-disk algorithm on an alternating knot that you provide.
If you are already familiar with the KLO interface, knots are entered as usual, and the key sequence
ctrl-B executes the search; click on each step to see a screenshot.]
- Create a new document, either by clicking the top-left icon for a blank page, or via
Knot to sketch a knot (you may also choose to enter it as a braid, if you like).
Ok to continue.
- Move the mouse with its button down to draw; you may select and delete pieces of your drawing via
Select and the
Delete key. You may hold
shift as you draw to undercross in general, but there is no need to do so here, as we will make the whole diagram alternating in a later step.
Process to continue.
Alternate to alternate the crossings.
- Then press
Accept to finish.
- Optionally, click the
refresh icon to clean up the diagram.
- With a diagram in hand, press
cmd-B on a Mac) to run the algorithm—note that for large and/or composite knots, this can take some time. Three different results are possible: