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Finite orbits for nilpotent actions on the torus


Authors: S. Firmo and J. Ribón
Journal: Proc. Amer. Math. Soc. 146 (2018), 195-208
MSC (2010): Primary 37E30, 37E45, 37A15, 37A05, 54H20; Secondary 55M20, 37C25
DOI: https://doi.org/10.1090/proc/13686
Published electronically: August 1, 2017
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Abstract:

A homeomorphism of the $ 2$-torus with Lefschetz number different from zero has a fixed point. We give a version of this result for nilpotent groups of diffeomorphisms. We prove that a nilpotent group of $ 2$-torus diffeomorphims has finite orbits when the group has some element with Lefschetz number different from zero.


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Additional Information

S. Firmo
Affiliation: Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Mário Santos Braga s/n - Valonguinho, 24020-140 Niterói, Rio de Janeiro, Brasil
Email: firmo@mat.uff.br

J. Ribón
Affiliation: Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Mário Santos Braga s/n - Valonguinho, 24020-140 Niterói, Rio de Janeiro, Brasil
Email: javier@mat.uff.br

DOI: https://doi.org/10.1090/proc/13686
Keywords: Rotation vector, global fixed point, derived group, homeomorphism, diffeomorphism, nilpotent group, Lefschetz number, finite orbit
Received by editor(s): October 4, 2016
Received by editor(s) in revised form: January 26, 2017, and February 3, 2017
Published electronically: August 1, 2017
Additional Notes: This work was supported in part by CAPES
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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