Computing the fundamental group of a higher-rank graph

Autor:	Kang, Sooran, Pask, David, Webster, Samuel B. G.
Rok vydání:	2013
Předmět:	Mathematics - Dynamical Systems Mathematics - Combinatorics Mathematics - Operator Algebras 14F35
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1310.7651 Zobrazit plný text záznamu View this record from Arxiv