OAI/Topology/ArtinGroups/ParabolicIntersections/VisualTrivialSegment.lean
2 declarations, 0 contain sorry, 0 declared as axioms
The visual tree has a segment with trivial pointwise stabilizer. This proves the segment step in CMMW (2026), Theorem 3.2, using the unconditional parabolic intersection theorem and rank descent.
- lemma
OAI.HarmonicArtin.ParabolicIntersections.visual_pair_isParabolicline 19 - theorem
OAI.HarmonicArtin.ParabolicIntersections.visual_exists_trivial_pairline 28Source documentation
A finite segment of the genuine Bass--Serre tree has trivial stabilizer.
theorem visual_exists_trivial_pair (hIrred : IsIrreducible M) : ∃ u v : VisualVertex M Y Z, u≠v ∧ pairStabilizer (G := Artin M) u v=⊥ := by …Mentions: OAI.HarmonicArtin.ParabolicIntersections.IsIrreducible, OAI.HarmonicArtin.ParabolicIntersections.VisualVertex, OAI.HarmonicArtin.Artin