||A pair of symmetries (σ, τ ) of a Riemann surface X is said to be perfect if their product belongs to the derived subgroup of the group Aut+(X) of orientation preserving automorphisms. We show that given g 6= 2, 3, 5, 7 there exists a Riemann surface X of genus g admitting a perfect pair of symmetries of certain topological type. On the other hand we show that a twist can be written as a product of two symmetries of the same type which leads to a decomposition of a twist as a product of two commutators: one from M0 which entirely lives on a Riemann surface and one from M±0 . As a result we obtain the perfectness of the mapping class group Mg for such g relying only on results of Birman  but not on influential paper of Powell  nor on Johnson’s rediscovery of Dehn lantern relation  and nor on recent results of Korkmaz-Ozbagci  who found explicit presentation of a twist as a product of two commutators.
||Tots els drets reservats.
||Article ; recerca ; article ; publishedVersion
Mapping class group ;
Symmetries of Riemann surfaces
||Publicacions matematiques, V. 48 N. 1 (2004) , p. 103-106, ISSN 0214-1493