Boundary Slopes of 2-Bridge Links
In their paper The space of
incompressible surfaces in a 2-bridge link complement, Trans.
Amer. Math. Soc. 305(2):575-599, 1988, Floyd
and Hatcher explicitly describe all incompressible surfaces in the
complement of a 2-bridge link. However, they do not compute the
boundary slopes of these surfaces, saying only that it should be
possible in principle. In his (unpublished) dissertation, Lash
developed an algorithm based on Floyd and Hatcher's work for computing
the boundary slopes of 2-bridge links.
This webpage contains two
- A link to the paper Computing
boundary slopes of 2-bridge links by Hoste and Shanahan.
In this paper Lash's algorithm is improved by eliminating several
computationally intensive steps, and a table is given of boundary
slopes for all 2-bridge links up to 10 crossings.
- The computer program used to create the table in this paper.
Computing boundary slopes of 2-bridge
links is available from the arXiv math.GT/0505442.
The program can compute the boundary slopes of a two-bridge link. The
program is written in the programming language
Python. You will need a Python interpreter (version 1.5 or newer) to
run the program. 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
To install, download the proper file:
To run the file in:
The program will then give you all the instructions you will need.
- UNIX (e.g. Linux, or terminal shell in Mac OS X): While in the
directory where you
put the file, type python bdyslopes.py
- Mac OS X with PythonIDE: Launch PythonIDE and open bdyslopes.py. Next, go
to the right arrow at the top of the scroll bar and choose "Run as Main". Finaly,
click "run all."
- Windows Double-click the file and it will run as an application.
Send comments or problems to
Jim Hoste or