MathDBPitts–Rubinstein conjecture on strongly irreducible Heegaard surfaces
Pitts–Rubinstein conjecture on strongly irreducible Heegaard surfaces
Let a strongly irreducible Heegaard surface lie in a Riemannian three-manifold. Pitts–Rubinstein conjecture. It is either isotopic to a minimal surface of index at most , or isotopic after a single compression to the boundary of a tubular neighborhood of a stable one-sided Heegaard surface. This conjecture was recently resolved and underlies effective finiteness results for irreducible Heegaard splittings.
Sources & referencesView supporting material
Primary source
Tobias Holck Colding, David Gabai and Daniel Ketover, “Geometric Methods In Heegaard Theory”, arXiv:2002.00445 (2020).
Additional references
2 papers in this index state this conjecture (2019–2020). The statement above is taken from the most recent of them; the others are arXiv:1911.07161.
Progress summary
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