Fixed points of discrete nilpotent group actions on S2
Suely Druck, Fuquan Fang, Sebastiao Firmo
Abstract
We prove that for each integer k of at least 2, there is an open neigborhood νk 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 νk, 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.
Create a lesson
Related papers
Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers
Nicolas Bridges, Shawn Cui, Nathan Geer
3-manifold decision problems and Riemann hypotheses
John A. Baldwin, Steven Sivek
On the (in)finiteness of fixed characters in genus 3
Yixuan Fu
Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds
Alexander Kolpakov
Convex ribbon disks, quasipositivity, and Lagrangian sliceness
Joseph Breen, Alexander Zupan
A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds
Maria Morariu