On the complexity of non-orientable Seifert fibre spaces

Alessia Cattabriga; Sergei Matveev; Michele Mulazzani; Timur Nasybullov

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arXiv · 1704.06721

On the complexity of non-orientable Seifert fibre spaces

Alessia Cattabriga·Sergei Matveev·Michele Mulazzani·Timur Nasybullov

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Abstract

In this paper we deal with Seifert fibre spaces, which are compact 3-manifolds admitting a foliation by circles. We give a combinatorial description for these manifolds in all the possible cases: orientable, non-orientable, closed, with boundary. Moreover, we compute a potentially sharp upper bound for their complexity in terms of the invariants of the combinatorial description, extending to the non-orientable case results by Fominykh and Wiest for the orientable case with boundary and by Martelli and Petronio for the closed orientable case.

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Alessia Cattabriga, Sergei Matveev, Michele Mulazzani, Timur Nasybullov. 2018-02-26. On the complexity of non-orientable Seifert fibre spaces. https://arxiv.org/abs/1704.06721

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