JSJ decompositions and polytopes for two-generator one-relator groups

2021/01/06 by Gardam, Giles, Kielak, Dawid, Logan, Alan D. · 1 citation
#20E34 #20F05 #20F65 #20F67 #20J05 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2101.02193

Abstract

We provide a direct connection between the Z_max (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianisation of rank 2. We deduce various structural and algorithmic properties, like the existence of a quadratic-time algorithm computing the Z_max-JSJ decomposition of such groups.

Cited by

• The word problem for two-generator one-relator inverse monoids

Related

• Effective JSJ Decompositions
• Automorphisms of Groups and a Higher Rank JSJ Decomposition II: The single ended case
• Automorphisms of Groups and a Higher Rank JSJ Decomposition I: RAAGs and a Higher Rank Makanin-Razborov Diagram
• Two-generator one-relator groups and marked polytopes
• JSJ decompositions: definitions, existence, uniqueness. I: The JSJ\n deformation space