The minimally displaced set of an irreducible automorphism of FN is co-compact

被引：0

作者：

Francaviglia, Stefano ^{[1
]}

Martino, Armando ^{[2
]}

Syrigos, Dionysios ^{[2
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Bologna, Italy

[2] Univ Southampton, Math Sci, Southampton, Hants, England

来源：

ARCHIV DER MATHEMATIK | 2021年 / 116卷 / 04期

关键词：

Automorphisms of tree groups; Culler-Vogtmann space; Outer space; Minimally displacement set; Lipschitz metric; Irreducible automorphism; Exponential growth; Growth rate one; Centralisers;

D O I：

10.1007/s00013-021-01579-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 phi, under the action of the centraliser C(phi). As a corollary, we get that the same holds for the action of <phi> on Min(phi). Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.

引用

页码：369 / 383

页数：15

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