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Computing the fundamental group of a higher-rank graph

Part of: (Co)homology theory Categories with structure

Published online by Cambridge University Press:  26 August 2021

Sooran Kang ,
David Pask  and
Samuel B.G. Webster
Sooran Kang
Affiliation:
College of General Education, Chung-Ang University, Seoul06974, Republic of Korea (sooran09@cau.ac.kr)
David Pask
Affiliation:
School of Mathematics and Applied Statistics, The University of Wollongong, Wollongong, NSW2522, Australia (dpask@uow.edu.au)
Samuel B.G. Webster
Affiliation:
Independent Hospital Pricing Authority, Level 6, 1 Oxford Street, Sydney, NSW2000, Australia (sbgwebster@gmail.com)
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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 higher-rank graphs when we show that the abelianization of the 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.

Keywords

Higher-rank graphfundamental group

MSC classification

Primary: 14F35: Homotopy theory; fundamental groups
Secondary: 18D99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 3 , August 2021 , pp. 650 - 661
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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