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.
|Number of pages||17|
|Journal||New York Journal of Mathematics|
|State||Published - 18 Mar 2017|
Bibliographical noteFunding Information:
The first author is supported by ISF 1941/14. Both authors acknowledge support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 “RNMS: Geometric structures And Representation varieties” (the GEAR Network).!
© 2017, University at Albany. All rights reserved.
- Axis bundle
- Outer space
ASJC Scopus subject areas
- Mathematics (all)