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arXiv · 1310.7651

Computing the fundamental group of a higher-rank graph

Sooran Kang·David Pask·Samuel B. G. Webster
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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 $k$-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.

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Sooran Kang, David Pask, Samuel B. G. Webster. 2013-10-29. Computing the fundamental group of a higher-rank graph. https://arxiv.org/abs/1310.7651

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