2 problems

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Algebraic torsion conjecture for contact manifolds containing glued Giroux domains
Algebraic torsion conjecture. Then $(V,\xi)$ has algebraic $1$ -torsion, and it is also algebraically overtwisted if $N$ contains any blown down boundary components.
Conjectureopencontact-geometry fillability symplectic-field-theoryarXiv posted 2 days ago
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The convex-fillability characterization of contact-type embeddability
Let $\Xi(3)$ denote the collection of closed $3$ --manifolds with positive, cooriented contact structures. Let $\Xi_{\text{\textsf{embed}}}(3)$ consist of those $(M,\xi)\in\Xi(3)$ t…
Conjectureopencontact-geometry fillability symplectic-4-manifoldsarXiv posted 2 days ago

Algebraic torsion conjecture for contact manifolds containing glued Giroux domains