Abstract
Let be a free group of positive, finite rank and let be a polynomial-growth automorphism. Then is strongly thick of order , where is the rate of polynomial growth of . This fact is implicit in work of Macura, whose results predate the notion of thickness. Therefore, in this note, we make the relationship between polynomial growth of and thickness explicit. Our result combines with a result independently due to Dahmani–Li, Gautero–Lustig, and Ghosh to show that free-by-cyclic groups admit relatively hyperbolic structures with thick peripheral subgroups.
Citation
Mark Hagen. "A remark on thickness of free-by-cyclic groups." Illinois J. Math. 63 (4) 633 - 643, December 2019. https://doi.org/10.1215/00192082-7917878
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