Classification of tight contact structures on some Seifert fibered manifolds: I

Tanushree Shah

Classification of tight contact structures on some Seifert fibered manifolds: I

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arxiv 2303.09490 v2 pith:AXFTCVGG submitted 2023-03-16 math.GT

Tanushree Shah This is my paper · ORCID

classification math.GT

keywords contactstructuresboundmanifoldssometightclassificationclassify

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We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory to obtain the upper bound.

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Bordered contact invariants and half Giroux torsion
math.GT 2025-06 conditional novelty 8.0 of 10

Separating half Giroux torsion does not force the contact invariant to vanish: infinitely many closed counterexamples exist, disproving Ghiggini's conjecture.

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