A presentation for a group of automorphisms of a simplicial complex
Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 331-337
Voir la notice de l'article provenant de la source Cambridge University Press
The Bass–Serre theorem supplies generators and relations for a group of automorphisms of a tree. Recently K. S. Brown [2] has extended the result to produce a presentation for a group of automorphisms of a simply connected complex, the extra ingredient being relations which come from the 2-cells of the complex. Suppose G is the group, K the complex and L the 1-skeleton of K. Then an extension of π1(L) by G acts on the universal covering space of L (which is of course a tree) and Brown's technique is to apply the work of Bass and Serre to this action. Our aim is to give a direct elementary proof of Brown's theorem which makes no use of covering spaces, deals with the Bass–Serre theorem as a special case and clarifies the roles played by the various generators and relations.
A presentation for a group of automorphisms of a simplicial complex. Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 331-337. doi: 10.1017/S0017089500007424
@misc{10_1017_S0017089500007424,
title = {A presentation for a group of automorphisms of a simplicial complex},
journal = {Glasgow mathematical journal},
pages = {331--337},
year = {1988},
volume = {30},
number = {3},
doi = {10.1017/S0017089500007424},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007424/}
}
[1] 1.Armstrong, M. A., Trees, tail wagging and group presentations, L'Enseignement Mathematique 32 (1986), 261–270. Google Scholar
[2] 2.Brown, K. S., Presentations for groups acting on simply connected complexes, J. Pure and Applied Algebra 32 (1984), 1–10. Google Scholar | DOI
[3] 3.Serre, J.-P., Arbres, Amalgames, SL, Astérisque 46 (Soc. Math, de France 1977). Google Scholar
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