International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 47381, 15 pages
doi:10.1155/IJMMS/2006/47381

The fundamental group and Galois coverings of hexagonal systems in 3-space

J. A. De La Peña1 and L. Mendoza2

1Instituto de Matemáticas, Universidad Nacional Autonoma de Mexico, Cd. Universitaria, México 04510 DF, Mexico
2Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, Mérida 5101, Venezuela

Received 10 August 2005; Revised 1 August 2006; Accepted 11 October 2006

Copyright © 2006 J. A. De La Peña and L. Mendoza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider hexagonal systems embedded into the 3-dimensional space ℝ3. We define the fundamental group π1(G) of such a system G and show that in case G is a finite hexagonal system with boundary, then π1(G) is a (non-Abelian) free group. In this case, the rank of π1(G) equals m(G)−h(G)−n(G)+1, where n(G) (resp., m(G), h(G)) denotes the number of vertices (resp., edges, hexagons) in G.