MathDBSeifert-fibre-edge conjecture for one-vertex triangulations of small Seifert fibre spaces
Seifert-fibre-edge conjecture for one-vertex triangulations of small Seifert fibre spaces
A Seifert fibre space is a 3-manifold fibred by circles in the Seifert sense, and a small Seifert fibre space is one that contains no embedded two-sided incompressible surfaces. An edge is isotopic to a Seifert fibre when the embedded closed curve it realizes is isotopic to one of the circle fibres.
Seifert-fibre-edge conjecture. Every one-vertex triangulation of a small Seifert fibre space has an edge isotopic to a Seifert fibre.
Small Seifert fibre spaces are important pieces in JSJ and geometric decompositions, but their lack of embedded two-sided incompressible surfaces makes them difficult to study. The paper presents this as an unresolved conjecture motivating its search for counterexamples.
Sources & referencesView supporting material
Primary source
Benjamin A. Burton and Alexander He, “Finding large counterexamples by selectively exploring the Pachner graph”, arXiv:2303.06321 (2024).
Additional references
3 papers in this index state this conjecture (2007–2023). The statement above is taken from the most recent of them; the others are arXiv:1202.4142, arXiv:math/0703276.
Progress summary
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