Elements of finite order in the fundamental group of a branched cyclic covering (Q1085833)

Main theorem: Let M be a connected q-dimensional P.L. manifold, and \(\tilde L\subset \overset\circ M\) a locally flat, codimension two, submanifold. Suppose that \(\phi\) is a periodic automorphism of M of order h, whose fixed-point set is \(\tilde L.\) Assume that: (1) \(\phi\) induces the identity on \(\pi_ 1(M)\); (2) \(\pi_ 1(M)\not\cong \pi_ 1(M/\phi)\). Then there is in \(\pi_ 1(M)\) a non-trivial element whose order divides h. The theorem is proved using a process for obtaining a presentation of \(\pi_ 1(M)\) due to \textit{R. H. Fox} [Ann. Math., II. Ser. 64, 407-419 (1956; Zbl 0073.254)].