Ribbon Disks for Alternating Knots


The  paper, by Lucia Karageorghis (Undergraduate at the University of Durham) and Frank Swenton (Middlebury College), presenting the details of this computation and the mathematics from which it arose, is currently avavailable on arXiv. Please cite any use of these results via that paper:


The results of the computation are provided below, and the data files provided can be opened with the KLO software.

Data files

The following file exhibits the explicit sequences of oriented saddle moves establishing upper bounds in the paper above (where necessary). It is downloadable via the link below in zipped format; after unzipping, the file results.rb can be opened in KLO in the Ribbon Disks dialog, which is accessed via the main menu Computation → Ribbon Disks. In the tree view presented, a knot can be double-clicked to open up the relevant diagram [sequence] as a new KLO document.

69kb .zip file