We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our results fit naturally into the suite of known geometrical results about $k$-graphs when we show that the abelianisation of fundamental group is the homology group. We end with a calculation which gives a non-standard presentation of the fundamental group of the Klein bottle to the one normally found in the literature.
- Pub Date:
- October 2013
- Mathematics - Dynamical Systems;
- Mathematics - Combinatorics;
- Mathematics - Operator Algebras;
- Dynamical content from 1310.7651 removed. Content on fundamental group revised, and improved with new examples and error in example at end of recent submission