# Dehn functions of subgroups of right-angled Artin groups

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## Abstract

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 \(n^{k+2}\).

## Keywords

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## Notes

### Acknowledgements

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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