Finiteness of the topological rank of diffeomorphism groups

Abstract

For a compact smooth manifold M (with boundary) we prove that the topological rank of the diffeomorphism group Diff k 0 (M ) (Diff k 0 (M, ∂M )) is finite for all k ≥ 1. This extends a result from [2] where the same claim is proved in the special case of dimM = k = 1.