International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 18, Pages 47381, 15 p.
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
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.