Boundary slopes of Montesinos knots
Hatcher and Oertel in their paper Boundary slopes of
Montesinos knots gave an algorithm for computing the boundary
slopes of a given Montesinos knot. At the end of their paper,
they provided a table which gave the boundary slopes for each knot
of 10 or fewer crossings which is a Montesinos knot.
Unfortunately, this table contains several errors. This page
provides two things.
- A short paper containing a corrected table.
- The computer programs used to create the table in this
Important Note: Prior to January 2, 2008 this program
contained a number of bugs. The current version is most likely
correct. The below paper was revised with the new program in June
is available from the arXiv, and was revised in June 2010.
The program can compute the boundary slopes of a two-bridge
knot or Montesinos knot. The program is written in the
programming language Python. You will need a Python
interpreter (version 1.5 or newer) to run these programs.
These are free and available for virtually every platform from
the Python home page. If
you're using UNIX, you can see if your system has python
installed by typing which python (Linux systems
almost always have Python installed).
To install, download all the files below into the same directory
(folder). Then do
The program will then give you all the instructions you will
Here are the files you'll need:
For those using a command-line based operating system, such as UNIX,
and prefer a command line version of bdry_run.py, I offer:
(instructions at the top of each file)
- UNIX (e.g. Linux, Mac OS X): While in the directory where you put all the files,
type python bdry_run.py
- Mac OS 9: Run the Python program BuildApplet on
bdry_run.py to create an executable. (Old versions of
MacPython: Drag the file bdry_run.py and drop it onto the main
- Windows: Double click the file bdry_run.py. If
this doesn't work, try the instructions for Mac OS.
Send comments and problems to Nathan Dunfield