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Computing the fundamental group of a higher-rank graph

Journal Article


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.

Publication Date


  • 2021

Citation


  • Kang, S., Pask, D., & Webster, S. B. G. (2021). Computing the fundamental group of a higher-rank graph. Proceedings of the Edinburgh Mathematical Society, 64(3), 650-661. doi:10.1017/S0013091521000420

Scopus Eid


  • 2-s2.0-85113668240

Web Of Science Accession Number


Start Page


  • 650

End Page


  • 661

Volume


  • 64

Issue


  • 3

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.

Publication Date


  • 2021

Citation


  • Kang, S., Pask, D., & Webster, S. B. G. (2021). Computing the fundamental group of a higher-rank graph. Proceedings of the Edinburgh Mathematical Society, 64(3), 650-661. doi:10.1017/S0013091521000420

Scopus Eid


  • 2-s2.0-85113668240

Web Of Science Accession Number


Start Page


  • 650

End Page


  • 661

Volume


  • 64

Issue


  • 3