New York Journal of Mathematics
Volume 23 (2017) 365-381


Yael Algom-Kfir and Catherine Pfaff

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

view    print

Published: March 18, 2017
Keywords: Out(Fn), Outer Space, axis bundle
Subject: 20E36

We let φ be an ageometric fully irreducible outer automorphism 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.


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).

Author information

Yael Algom-Kfir:
Department of Mathematics, University of Haifa, Mount Carmel, Haifa, 31905, Israel

Catherine Pfaff:
Department of Mathematics, University of California at Santa Barbara, South Hall, Room 6607, Santa Barbara, CA 93106-3080