On polynomial free-by-cyclic groups

Jean Pierre Mutanguha

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arXiv · 2412.16150

On polynomial free-by-cyclic groups

Jean Pierre Mutanguha

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Abstract

A free-by-cyclic group can often be viewed as a mapping torus of a free group automorphism (monodromy) in multiple ways. What dynamical properties must these monodromies share, and to what extent are they invariant under quasi-isometries? We give a new proof using cyclic splittings that the growth type of a monodromy is a geometric invariant of the free-by-cyclic group; we also characterise the degree of polynomial growth using slender splittings. For exponential growth, we conjecture that the nesting of attracting laminations is a geometric invariant.

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BibTeX RIS

Jean Pierre Mutanguha. 2024-12-20. On polynomial free-by-cyclic groups. https://arxiv.org/abs/2412.16150

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