Involutions in surface mapping class groups
As first result it is proved that the mapping class group M(F) of a closed orientable surface F of genus \(g>2\) is generated by involutions (elements of order 2). Then the possible types of the product of two involutions in M(F) are analysed, by considering the action of M(F) on the Thurston-compactification K of the Teichmüller space \(T\subset K\) of F. According to the relative position of the fixed point sets of the 2 involutions, such a product will be of finite order (common fixed point in T), reducible (common fixed point in K but not in T) or pseudo-Anosov (no common fixed point), in strong analogy to the possible types of the product of two elliptic involutions on the Poincaré-disc (elliptic, parabolic or hyperbolic).
Thurston-compactification of the Teichmüller space
mapping class group of a closed orientable surface
scientific article; zbMATH DE number 4069834