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Yael Algom-Kfir and Catherine Pfaff
Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms view print
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| Published: |
March 18, 2017
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| Keywords: |
Out(Fn), Outer Space, axis bundle |
| Subject: |
20E36 |
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Abstract
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.
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| Acknowledgements
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).
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| Author information
Yael Algom-Kfir:
Department of Mathematics, University of Haifa, Mount Carmel, Haifa, 31905, Israel
yalgom@univ.haifa.ac.il
Catherine Pfaff:
Department of Mathematics, University of California at Santa Barbara, South Hall, Room 6607, Santa Barbara, CA 93106-3080
cpfaff@math.ucsb.edu
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