For an orderable Legendrian class with a positive Legendrian loop that extends to a contact loop, an unbounded invariant distance exists even when no positive contact loop exists.
Symplectic Geom.16 (2018), no
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Invariant distances on spaces of Legendrians
For an orderable Legendrian class with a positive Legendrian loop that extends to a contact loop, an unbounded invariant distance exists even when no positive contact loop exists.