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

摘要

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.