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Decomposition of the vertex group of 3-manifolds

✍ Scribed by Louis Kauffman; Sóstenes Lins

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
432 KB
Volume
103
Category
Article
ISSN
0012-365X

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✦ Synopsis

Kauffman, L. and S. Lins, Decomposition of the vertex group of 3-manifolds, Discrete Mathematics 103 (1992) 49-55. The vertex group c(M) of a closed PL n-manifold is an invariant obtained from a crystallization representing M (see Ferri and Gaghardi (1982)). These groups are introduced by Lins (1989) where their topological invariance is proved. In this note we propose, for n = 3 to illuminate the connection of 5 and the fundamental group n,. We show, as suspected in [8], that for every closed 3-manifold M3, E(M3) = n,(M3) * n,(M3) * n,(M3) * F, where F is a free group in one generator.

The present proof does not seem to (dptly) generalize for higher dimensions.

The result also opens the possibility of searching for topologically invariant automorphisms of E. Such automorphisms could give significant information about the manifold M3.

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