On $\mathbb{Z}_2$-Thurston norms and pseudo-horizontal surfaces in orientable Seifert $3$-manifolds

Xiaoming Du

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arXiv · 2101.11154

On $\mathbb{Z}_2$-Thurston norms and pseudo-horizontal surfaces in orientable Seifert $3$-manifolds

Xiaoming Du

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Abstract

We describe a general method to compute the $\mathbb{Z}_2$-Thurston norm for every $\mathbb{Z}_2$-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 $\mathbb{Z}_2$-homology classes. We then describe an algorithm to calculate the $\mathbb{Z}_2$-Thurston norm of each $\mathbb{Z}_2$-homology classes. We also present several interesting examples.

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BibTeX RIS

Xiaoming Du. 2021-01-27. On $\mathbb{Z}_2$-Thurston norms and pseudo-horizontal surfaces in orientable Seifert $3$-manifolds. https://arxiv.org/abs/2101.11154

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