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arXiv · 2411.19887

Non-orderability and the contact Hofer norm

Jakob Hedicke·Egor Shelukhin
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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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Jakob Hedicke, Egor Shelukhin. 2024-11-29. Non-orderability and the contact Hofer norm. https://arxiv.org/abs/2411.19887

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