COMMUTATORS OF $C^R$-DIFFEOMORPHISMS ACTING ALONG LEAVES

Tomasz Rybicki

Key words: Group of diffeomorphisms, identity component,
        commutator, perfectness of groups, foliation.

1991 Math. Subject Classification: Primary 58D05, Secondary 22E65.

Abstract: We study whether a $C^r$-diffeomorphism
which is isotopic to the identity and preserves leaves of a foliation
can be written as a product of commutators. The result and techniques
depend on the class $C^r$, where $0\leq r\leq \infty$.