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

J. A. De La Peña and L. Mendoza

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-15

Abstract:

We consider hexagonal systems embedded into the 3 -dimensional space ℝ 3 . We define the fundamental group π 1 ( G ) of such a system G and show that in case G is a finite hexagonal system with boundary, then π 1 ( G ) is a (non-Abelian) free group. In this case, the rank of π 1 ( 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 .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:047381

DOI: 10.1155/IJMMS/2006/47381

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