Computing the fundamental group of a higher-rank graph
Dynamical Systems
2020-09-10 v3 Combinatorics
Operator Algebras
Abstract
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 -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.
Cite
@article{arxiv.1310.7651,
title = {Computing the fundamental group of a higher-rank graph},
author = {Sooran Kang and David Pask and Samuel B. G. Webster},
journal= {arXiv preprint arXiv:1310.7651},
year = {2020}
}
Comments
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