Computing the fundamental group of a higher-rank graph. Issue 3 (26th August 2021)

• Record Type: Journal Article
• Authors: Kang, Sooran; Pask, David; Webster, Samuel B.G.
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 64:Issue 3(2021)
• Page Start: 650
• Page End: 661
• Publication Date: 2021-08-26
• Subjects: Higher-rank graph -- fundamental group; 14F35 -- 18D99; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091521000420
• Languages: English
• ISSNs: 0013-0915

Abstract

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.