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Invariant distances on spaces of Legendrians

Published 24 Jul 2025 in math.SG and math.DG | (2507.18724v1)

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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