A Note on Commuting Diffeomorphisms on Surfaces
arXiv:math/0408010 · doi:10.1088/0951-7715/18/4/005
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".
arXiv comment16 pages