In McDuff and torus bundle Liouville domains, every weakly exact Lagrangian torus is homotopic to a standard fibre, and any exact Lagrangian meeting two different boundary components has non-zero wrapped Floer cohomology.
Non-orderability and the contact Hofer norm
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abstract
We relate non-orderability in contact topology to shortening in the contact Hofer norm. Combined with considerations of open books, this provides many new examples of non-orderable contact manifolds, including contact boundaries of subcritical Weinstein domains, and in particular the long-standing case of the standard $S^1 \times S^2.$ We also produce new examples of contact manifolds admitting contactomorphisms without translated points, provide obstructions to subcritical polarizations of symplectic manifolds, and establish a $\mathcal{C}^0$-continuity property of the contact Hofer metric.
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On weakly exact Lagrangians in Liouville bi-fillings
In McDuff and torus bundle Liouville domains, every weakly exact Lagrangian torus is homotopic to a standard fibre, and any exact Lagrangian meeting two different boundary components has non-zero wrapped Floer cohomology.