The fixed subgroups of homeomorphisms of Seifert manifolds

Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold B M , and f . : . 1(M) . . 1(M) be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of f . , namely, rankFix(f . ) < 2rank. 1(M), which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.