Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms

Yael Algom-Kfir; Catherine Pfaff

Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We let φ be an ageometric fully irreducible outer automor- phism so that its Handel-Mosher axis bundle (Handel and Mosher, 2011) consists of a unique axis (as in Mosher and Pfaff. 2016). We show that the centralizer Cen(〈φ〉) of the cyclic subgroup generated by φ equals the stabilizer Stab(Λ_φ⁺) of the attracting lamination Λ_φ⁺ and is isomorphic to ℤ. We further show, via an analogous result about the commensurator, that the normalizer N(〈φ〉) of (φ) is isomorphic to either ℤ or ℤ₂*ℤ₂.

Original language	English
Pages (from-to)	365-381
Number of pages	17
Journal	New York Journal of Mathematics
Volume	23
State	Published - 18 Mar 2017

Bibliographical note

Publisher Copyright:
© 2017, University at Albany. All rights reserved.

Keywords

Axis bundle
Out(F)
Outer space

ASJC Scopus subject areas

General Mathematics

Cite this

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AB - We let φ be an ageometric fully irreducible outer automor- phism so that its Handel-Mosher axis bundle (Handel and Mosher, 2011) consists of a unique axis (as in Mosher and Pfaff. 2016). We show that the centralizer Cen(〈φ〉) of the cyclic subgroup generated by φ equals the stabilizer Stab(Λφ+) of the attracting lamination Λφ+ and is isomorphic to ℤ. We further show, via an analogous result about the commensurator, that the normalizer N(〈φ〉) of (φ) is isomorphic to either ℤ or ℤ2*ℤ2.

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Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this