On the uniform perfectness of the groups of diffeomorphisms of even-dimensional manifolds

  • Takashi Tsuboi

    University of Tokyo, Japan

Abstract

We show that the identity component Diff of the group of diffeomorphisms of a compact -dimensional manifold (, ) is uniformly perfect for , i.e., any element of Diff can be written as a product of a bounded number of commutators. It is also shown that for a compact connected manifold (), the identity component Diff of the group of diffeomorphisms of (, ) is uniformly simple, i.e., for elements and of Diffid, can be written as a product of a bounded number of conjugates of or .

Cite this article

Takashi Tsuboi, On the uniform perfectness of the groups of diffeomorphisms of even-dimensional manifolds. Comment. Math. Helv. 87 (2012), no. 1, pp. 141–185

DOI 10.4171/CMH/251