Finite orbits for nilpotent actions on the torus

Firmo, S.; Ribón, J.

doi:10.1090/proc/13686

Finite orbits for nilpotent actions on the torus
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by S. Firmo and J. Ribón PDF

Proc. Amer. Math. Soc. 146 (2018), 195-208 Request permission

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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