Fixed points of discrete nilpotent group actions on S^2
Geometric Topology
2007-05-23 v1 Algebraic Geometry
Differential Geometry
Dynamical Systems
Abstract
We prove that for each integer k of at least 2, there is an open neigborhood \nu_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 \nu_k, then the natural action on S^2 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.
Cite
@article{arxiv.math/0109015,
title = {Fixed points of discrete nilpotent group actions on S^2},
author = {Suely Druck and Fuquan Fang and Sebastiao Firmo},
journal= {arXiv preprint arXiv:math/0109015},
year = {2007}
}
Comments
15 pages, 2 figures