Algorithms and topology for Cayley graphs of groups
Abstract
Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. A comparison with automatic groups is given. Another characterization of autostackability is given in terms of prefix-rewriting systems. Every group which admits a finite complete rewriting system or an asynchronously automatic structure with respect to a prefix-closed set of normal forms is also autostackable. As a consequence, the fundamental group of every closed 3-manifold with any of the eight possible uniform geometries is autostackable.
Cite
@article{arxiv.1307.4981,
title = {Algorithms and topology for Cayley graphs of groups},
author = {Mark Brittenham and Susan Hermiller and Derek Holt},
journal= {arXiv preprint arXiv:1307.4981},
year = {2013}
}