We study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth ϕ, under the action of the centraliser C(ϕ). As a corollary, we get that the same holds for the action of < ϕ> on Min(ϕ). Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.
Francaviglia S., Martino A., Syrigos D. (2021). The minimally displaced set of an irreducible automorphism of FN is co-compact. ARCHIV DER MATHEMATIK, 116(4), 369-383 [10.1007/s00013-021-01579-z].
The minimally displaced set of an irreducible automorphism of FN is co-compact
Francaviglia S.
;
2021
Abstract
We study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth ϕ, under the action of the centraliser C(ϕ). As a corollary, we get that the same holds for the action of < ϕ> on Min(ϕ). Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.| File | Dimensione | Formato | |
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