Algorithms and topology of Cayley graphs for groups

JOURNAL OF ALGEBRA

卷:415

Article

Brittenham, Mark¹  Hermiller, Susan¹  Holt, Derek² 

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

关键词: Automatic group;    Rewriting system;    Word problem;    3-Manifold;   

DOI  :  10.1016/j.jalgebra.2014.06.001

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free