Incompressible surfaces in Seifert fibered spaces

Frohman (1986) showed that a nonorientable incompressible surface in a Seifert fibered space with orientable base and total spaces is isotopic to either a pseudo-horizontal or pseudo-vertical surface. The present author extends that result by removing the restrictions on the orientability of the base and total spaces and the surface. This result is used to determine the incompressible surfaces in S1-bundles up to homeomorphism, and to answer a question from the paper by End (1992).