Involutions on torus bundles over \(S^ 1\)
For a matrix A in GL(2,\({\mathbb{Z}})\), \(M_ A\) denotes the torus bundle over \(S^ 1\) whose monodromy matrix is A. As a consequence of theorems of this paper, the author obtains the estimate on the number of non- equivalent symmetries on torus bundles. That is, let \(Inv(M_ A)\) denote the set of all equivalence classes of involutions on \(M_ A\) and \(| S|\) denote the cardinality of S. Then, (1) if \(M_ A\) is an orientable torus bundle, then \(1\leq | Inv(M_ A)| \leq 21\). (2) If \(M_ A\) is a non-orientable torus bundle with tr(A)\(\neq 0\), then \(1\leq | Inv(M_ A)| \leq 7\).
scientific article; zbMATH DE number 3911321
scientific article