Subgroups of a free group with every growth rate

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arxiv 2505.10650 v1 pith:GVK4UEYS submitted 2025-05-15 math.GR

Michail Louvaris , Daniel T. Wise , Gal Yehuda This is my paper

classification math.GR

keywords alphaeverygrowthrateexistsfreegroupsubgroup

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For every $\alpha \in [1,2r-1]$, we show there exists a subgroup $H<F_r$ whose growth rate is $\alpha$.

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On the growth spectrum of hyperbolic groups
math.GR 2026-07 unverdicted novelty 6.0

For free and surface groups acting convex-cocompactly on hyperbolic spaces the growth spectrum is [0, ω_G]; for any hyperbolic group it contains [0, ω_G/2] (strictly larger if divergent).