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Algorithmic implementation of the solution to the word problem in Right-Angled Artin groups.

The goal of this thesis is to write a program which generates Cayley graphs of right-angled Artin groups. For this, the word problem must be solved. The particular method which we will use, namely pilings, was invented by J. Crisp, E. Godelle, and B. Wiest [1], however, I will first present my own variation of it which is more theoretical but, in my opinion, more intuitive in its functionality. It requires a statement about directed graphs for which I was unable to find a source, thus the proofs in Section 1.4 are my own.

The generated Cayley graphs were originally meant to be used in a machine learning project by F. Lopez, B. Pozzetti, S. Trettel, and A. Wienhard. Since right-angled Artin groups naturally have both free abelian and free subgroups, their Cayley graphs exhibit both flat and hyperbolic features, which makes them quite similar to real-world datasets and thus useful for the testing of graph embedding techniques.


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Year: 2021

Author : Jannis Heising

Prof. Dr. Beatrice Pozzetti