2013/07/18 by Mark Brittenham, Susan Hermiller, Brittenham, Mark +3
Mathematics · #20F10 #20F65 #68Q42 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F10 #msc:20F65 #msc:68Q42
paper · pdf · doi:10.48550/arxiv.1307.4981
arxiv created 2013/07/18 · arxiv updated 2013/07/19
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.