Contact Hofer norm bounds, obtained from open books and loose Legendrians, imply non-orderability and resolve the standard S^1 × S^2 case.
Hedicke , Lorentzian distance functions in contact geometry , Journal of Topology & Anal- ysis, 16 (2024)
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Non-orderability and the contact Hofer norm
Contact Hofer norm bounds, obtained from open books and loose Legendrians, imply non-orderability and resolve the standard S^1 × S^2 case.