Computing the fundamental group of a higherrank graph
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.7651
 Bibcode:
 2013arXiv1310.7651K
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Combinatorics;
 Mathematics  Operator Algebras;
 14F35
 EPrint:
 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