On genus actions of finite simple groups on handlebodies and bounded surfaces (Q2493430)

We define that the genus (handlebody genus, resp.) of a finite group \(G\) is the least genus of a closed orientable surface (a closed orientable 3-dimensional handlebody, resp.) on which \(G\) acts by orientation-preserving diffeomorphisms. Such an action on a surface or handlebody of least genus is called a genus action of \(G\). Generalizing analogous results [\textit{A. J. Woldar}, Ill. J. Math. 33, 438--450 (1989; Zbl 0654.20013); \textit{S. A. Broughton}, Pac. J. Math. 158, 23--48 (1993; Zbl 0823.57021)] for genus actions of finite simple groups on closed surfaces, the author proves that \(G\) is a normal subgroup of small index in the orientation-preserving isometry group \(H\) of \(V\), and that \(H\) is canonically isomorphic to a subgroup of the automorphism group of \(G\).