Abstract

We compute a presentation of the fundamental group of a higherrank graph
using a coloured graph description of higherrank 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
nonstandard presentation of the fundamental group of the Klein bottle to the
one normally found in the literature.