Article contents
A presentation for a group of automorphisms of a simplicial complex
Published online by Cambridge University Press: 18 May 2009
Extract
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1988
References
- 1
- Cited by