I released a program that should have been added to this site quite some time ago: comphom. It is a simple demo application that computes homology groups from simplicial triangulations.

People who have not yet heard anything about topology might not enjoy this as much as I do. Anyway, if you happen to stumble over any triangulation (such as those given by F. Lutz on his Manifold Page), comphom will compute the homology groups and write them to a file.

The program is available in the projects section of my homepage.

Let me outline how to use the program (the program package contains a README which is slightly more precise):

  • Compile the program via make. The Makefile should work for any POSIX-compatible operating system.
  • Download a triangulation from the Manifold Page (use the outdated lexicographic format).
  • Use the Perl script lex_convert.pl to convert the files into the format comphom understands: perl lex_convert.pl --input <file>
  • Start comphom: comphom --input <file>.ct [--output <file>.out]

It is also possible to compute homology groups for arbitrary triangulations. Just see the README for more information.

As always, I am grateful for any feedback about this particular project. Contact details are available elsewhere on this site (you can also find contact details in the source code).