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arXiv · 2507.18724

Invariant distances on spaces of Legendrians

Pierre-Alexandre Arlove
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Abstract

We construct new unbounded invariant distances on the universal cover of certain Legendrian isotopy classes. This is the first instance where unboundedness of an invariant distance is obtained without assuming the existence of a positive loop of contactomorphisms. We also show that invariant distances on Legendrian isotopy classes have to be discrete.

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Pierre-Alexandre Arlove. 2025-07-24. Invariant distances on spaces of Legendrians. https://arxiv.org/abs/2507.18724

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