Smooth perfectness through decomposition of diffeomorphisms into fiber preserving ones

2001/10/03 by Stefan Haller, Josef Teichmann · 1 citation
Mathematics · #math.DG #math.FA #msc:58D05

paper · pdf

published as Ann. Global Anal. Geom. 23(2003), 53--63.

arxiv created 2001/10/03 · arxiv updated 2009/11/30

Abstract

We show that on a closed smooth manifold M equipped with k fiber bundle structures whose vertical distributions span the tangent bundle, every smooth diffeomorphism f of M sufficiently close to the identity can be written as a product f=f₁... f_k, where f_i preserves the i^th-fiber. The factors f_i can be chosen smoothly in f. We apply this result to show that on a certain class of closed smooth manifolds every diffeomorphism sufficiently close to the identity can be written as product of commutators and the factors can be chosen smoothly. Furthermore we get concrete estimates on how many commutators are necessary.

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• Smooth perfectness of Hamiltonian diffeomorphism groups

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