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Involving symmetries of Riemann surfaces to a study of the mapping class group
Gromadzki, Grzegorz
Stukow, Michal

Data: 2004
Resum: 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 [1] but not on influential paper of Powell [6] nor on Johnson’s rediscovery of Dehn lantern relation [3] and nor on recent results of Korkmaz-Ozbagci [4] who found explicit presentation of a twist as a product of two commutators.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Mapping class group ; Symmetries of Riemann surfaces
Publicat a: Publicacions matematiques, V. 48 N. 1 (2004) , p. 103-106, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_48104_04


4 p, 82.4 KB

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