Fixed points of discrete nilpotent group actions on S2
Abstract
We prove that for each integer k of at least 2, there is an open neigborhood k of the identity map of the 2-sphere S2, in C1-topology such that: if G is a nilpotent subgroup of Diff1(S2) with length k of nilpotency, generated by elements in k, then the natural action on S2 has non-empty fixed point set. Moreover, the G-action has at least two fixed points if the action has a finite non-trivial orbit.
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