The fundamental group and Galois coverings of hexagonal systems in 3-space
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, wher...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/47381 |
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doaj-336fdb77450745f9975b3417798a18872020-11-24T23:55:12ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/4738147381The fundamental group and Galois coverings of hexagonal systems in 3-spaceJ. A. De La Peña0L. Mendoza1Instituto de Matemáticas, Universidad Nacional Autonoma de Mexico, Cd. Universitaria, México 04510 DF, MexicoDepartamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, Mérida 5101, VenezuelaWe 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.http://dx.doi.org/10.1155/IJMMS/2006/47381 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
J. A. De La Peña L. Mendoza |
| spellingShingle |
J. A. De La Peña L. Mendoza The fundamental group and Galois coverings of hexagonal systems in 3-space International Journal of Mathematics and Mathematical Sciences |
| author_facet |
J. A. De La Peña L. Mendoza |
| author_sort |
J. A. De La Peña |
| title |
The fundamental group and Galois coverings of hexagonal systems in 3-space |
| title_short |
The fundamental group and Galois coverings of hexagonal systems in 3-space |
| title_full |
The fundamental group and Galois coverings of hexagonal systems in 3-space |
| title_fullStr |
The fundamental group and Galois coverings of hexagonal systems in 3-space |
| title_full_unstemmed |
The fundamental group and Galois coverings of hexagonal systems in 3-space |
| title_sort |
fundamental group and galois coverings of hexagonal systems in 3-space |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2006-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/IJMMS/2006/47381 |
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