Torsion in (Gamma pi_2 K) / pi_1 K

This code was written for the bachelor thesis in mathematics with the topic "Torsion in ".

The PDF can be found here.

Author: Benjamin Ruppik (University of Bonn)

Date: June 8th, 2016

Supervisors: Dr. Daniel Kasprowski and Prof. Dr. Peter Teichner (Max Planck Institute for Mathematics in Bonn)

This is the Git-repository for publishing the bachelor thesis and the SageMath code.

Instructions

You will need SageMath to run this program (version 7.2 or above is recommended).

The relevant SageMath code is contained in the directory src/. Navigate there in your terminal, this directory should contain the file main.sage.

Now start SageMath in command line mode by typing sage, then load the main file via attach('main.sage').

The input for most of the relevant functions is the presentation of a finite, finitely presented group. See the corresponding SageMath documentation on how to enter such a presentation.

The function you probably want to use is

test_with_logging_and_progress(grouppresentation, grouppresentation_string)

Suppose G is a finitely presented group, then you would call this function as

test_with_logging_and_progress(G, "meaningful_name_for_G")

The function call creates two new files in the directory:

• meaningful_name_for_G_output.txt contains the results.
• meaningful_name_for_G_progress.txt is updated live to reflect the progress the program has made.

For examples see the bachelor thesis.

The program might take a very long time to process some group presentations, please be patient.