Dehn functions of subgroups of right-angled Artin groups

  • Noel Brady
  • Ignat SorokoEmail author
Original Paper


We show that for each positive integer k there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as \(n^k\). As a consequence we produce examples of right-angled Artin groups containing finitely presented subgroups whose Dehn functions grow as \(n^{k+2}\).


Dehn functions Right-angled Artin groups Free-by-cyclic groups Special cube complexes Growth of automorphisms 

Mathematics Subject Classification (2010)

Primary 20F65 20E05 20F67 57M20 



Noel Brady acknowledges support from NSF grant DMS 0906962 and Simons Foundation award 430097. Ignat Soroko also acknowledges support from Simons Foundation award 430097 and from the research assistantship of Dr. Jing Tao (NSF grant DMS 1611758 and NSF Career grant DMS 1651963). Both authors are grateful to Mark Hagen and Daniel Woodhouse for discussions about Gersten’s group. Finally, both authors are very grateful to the referee for valuable comments and suggestions which improved the quality of this paper.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OklahomaNormanUSA
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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