Abstract
Two-sided incompressible surfaces in Seifert fiber spaces with isolated singular fibers are well-understood. Frohman [3] and Rannard [6] have shown that one-sided incompressible surfaces in Seifert fiber spaces which have isolated singular fibers are either pseudo-horizontal or psuedo-vertical. We extend their result to characterise essential surfaces in Seifert fiber spaces which may have singular surfaces, i.e., in S1-foliated 3-manifolds which have fibered model neighbourhoods that are isomorphic to either a fibered solid torus or a fibered solid Klein bottle.
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