A Note on Commuting Diffeomorphisms on Surfaces
Dynamical Systems
2009-11-10 v3 Geometric Topology
Abstract
Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by any family of elements in V then the elements of G have common fixed points. This result generalizes a similar result due to Bonatti and announced in his paper "Diffeomorphismes commutants des surfaces et stabilite des fibrations en tores".
Cite
@article{arxiv.math/0408010,
title = {A Note on Commuting Diffeomorphisms on Surfaces},
author = {S. Firmo},
journal= {arXiv preprint arXiv:math/0408010},
year = {2009}
}
Comments
16 pages