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Fixed points of discrete nilpotent group actions on S 2

Suely Druck, Fuquan Fang, Sebastião Firmo (2002)

Annales de l’institut Fourier

We prove that for each integer k 2 there is an open neighborhood 𝒱 k of the identity map of the 2-sphere S 2 , in C 1 topology such that: if G is a nilpotent subgroup of Diff 1 ( S 2 ) with length k of nilpotency, generated by elements in 𝒱 k , then the natural G -action on S 2 has nonempty fixed point set. Moreover, the G -action has at least two fixed points if the action has a finite nontrivial orbit.

Flowability of plane homeomorphisms

Frédéric Le Roux, Anthony G. O’Farrell, Maria Roginskaya, Ian Short (2012)

Annales de l’institut Fourier

We describe necessary and sufficient conditions for a fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.

Flows of flowable Reeb homeomorphisms

Shigenori Matsumoto (2012)

Annales de l’institut Fourier

We consider a fixed point free homeomorphism h of the closed band B = × [ 0 , 1 ] which leaves each leaf of a Reeb foliation on B invariant. Assuming h is the time one of various topological flows, we compare the restriction of the flows on the boundary.

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