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A Note on Commuting Diffeomorphisms on Surfaces
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".Comment: 16 page
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