International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 47381, 15 pages
The fundamental group and Galois coverings of hexagonal systems in -space
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.
We consider hexagonal systems embedded into the -dimensional space . We define the fundamental group of such a system and show that in case is a finite hexagonal system with boundary, then is a (non-Abelian) free group. In this case, the rank of equals , where
(resp., , ) denotes the number of vertices (resp., edges, hexagons) in .