Polymake scripts for classification of 4-manifolds

These scripts for polymake operate on a census of 4-manifolds given as regina isomorphism signatures.

Prerequisites:

• Polymake
• GNU Parallel
• PostgreSQL
• GAP
• Regina

convert.sh

Converts the isomorphism signatures in the census to simplicial complexes

sql-populate.pl

Organizes the simplicial complexes in the census into a PostgreSQL database for easier management.

run-script-sql.pl

Runs a specified script on all triangulations that match a specific SQL query.

contract-bistellar.pl

Uses bistellar simplification to reduce the number of vertices in triangulations, resulting in a triangulation of a more manageable size.

empty_face_cutting.pl

Attempts to cut a connected sum of two manifolds into its constituent manifolds

random-discrete-morse-sql.pl

Attempts to find a spherical discrete morse vector on a given triangulation.

intersection_form.pl

Computes invariants of the intersection form and writes them into the SQL database

Computing fundamental groups

This is done running fundamental-group.pl to generate the files to feed into GAP. Then, run run-gap.sh to use GAP to simplify the group presentations, and run fp-group-presentation.pl to write these presentations into the database.

update_(PL)_homeomorphy.pl

These scripts attempt to find combinatorial isomorphisms (or PL-homeomorphisms in update_pl_homeomorphism.pl) between triangulations, and writes these into the database.