On Z2-Thurston norms and pseudo-horizontal surfaces in orientable Seifert 3-manifolds

We describe a general method to compute the Z(2)-Thurston norm for every Z(2) homology class in an orientable Seifert manifold with orientable orbit surface. Our main tools are pseudo-horizontal surfaces. We give a necessary and sufficient criterion for the existence of pseudo-horizontal surfaces, calculate the non-orientable genera for such surfaces, and detect their Z(2)-homology classes. We then describe an algorithm to calculate the Z(2)-Thurston norm of each Z(2)-homology classes. We also present several interesting examples. (c) 2022 Elsevier B.V. All rights reserved.