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.]

  1. Create a new document, either by clicking the top-left icon for a blank page, or via File→New
  2. Select Knot to sketch a knot (you may also choose to enter it as a braid, if you like).
  3. Click Ok to continue.
  4. 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.
  5. Press Process to continue.
  6. Press Alternate to alternate the crossings.
  7. Then press Accept to finish.
  8. Optionally, click the refresh icon to clean up the diagram.
  9. With a diagram in hand, press ctrl-B (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:
    1. Algorithmically ribbon
    2. Not ribbon
    3. Maybe ribbon