Finite subgroups of mapping class groups of geometric 3-manifolds
Let M be a compact Seifert fiber space which fibers over a euclidean or hyperbolic base-2-orbifold. Then M possesses a geometric structure modelled on \({\mathbb{H}}\) \(2\times {\mathbb{R}}\), \(SL_ 2\), \({\mathbb{E}}^ 3 \)or Nil, and the Teichmüller space T(M) of M has been determined in the previously reviewed paper: it is a euclidean space \({\mathbb{R}}^ n.\) As for surfaces, the mapping class group of M acts on T(M), and it is proved in the present paper, using the analogous result for surfaces due to \textit{S. P. Kerckhoff} [Ann. Math., II. Ser. 117, 235-265 (1983; Zbl 0528.57008)], that every finite subgroup G of the mapping class group has a fixed point in T(M). This implies that, under some restrictions, G can be realized by isometries of a geometric structure on M (in general, there is an algebraic obstruction for realizing G, see the paper by the reviewer in Manuscr. Math. 30, 361-373 (1980; Zbl 0438.57005).
Seifert fiber space which fibers over a euclidean or hyperbolic base-2- orbifold
finite subgroup G of the mapping class group
scientific article; zbMATH DE number 4038813