On the vertex group of n-manifolds |
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Authors: | Sóstenes Lins Michele Mulazzani |
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Institution: | (1) Departamento de Matemática da UFPE, Cidade Universitária, 50740-540 Recife, PE, Brazil;(2) Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy |
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Abstract: | In this paper we obtain the decomposition of the vertex group of n-manifolds, extending the one given by Kauffman and Lins for dimension 3 and solving the related conjecture. The result is obtained in the more general category of gems: the vertex group of a gem , representing an n-manifold M, is the free product of n copies of the fundamental group of M and a free group F of rank N–n, where N is the number of n-residues of . In particular, for crystallizations F Z and consequently the vertex group is an invariant of M. |
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Keywords: | 05C25 20F05 57M05 57M15 |
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