# 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 In his (unpublished) dissertation, Lash developed an algorithm based on Floyd and Hatcher's work for computing the boundary slopes of 2-bridge links.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 things:

• 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.

# Paper

Computing boundary slopes of 2-bridge links is available from the arXiv math.GT/0505442.

# Programs

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 Python installed). To install, download the proper file:
To run the file in:
• 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.
The program will then give you all the instructions you will need.

Send comments or problems to Jim Hoste or Patrick Shanahan