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arXiv · 2306.04612

Recognition of Seifert fibered spaces with boundary is in NP

Adele Jackson
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Abstract

We show that the decision problem of recognising whether a triangulated 3-manifold admits a Seifert fibered structure with non-empty boundary is in NP. We also show that the problem of producing Seifert data for a triangulation of such a manifold is in the complexity class FNP. We do this by proving that in any triangulation of a Seifert fibered space with boundary there is both a fundamental horizontal surface of small degree and a complete collection of normal vertical annuli whose total weight is bounded by an exponential in the square of the triangulation size.

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BibTeXRIS

Adele Jackson. 2023-06-07. Recognition of Seifert fibered spaces with boundary is in NP. https://doi.org/10.1007/s00208-024-02920-x

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