4 papers
Invariant distances on spaces of Legendrians
Pierre-Alexandre Arlove
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…
Contact non-squeezing in various closed prequantizations
Pierre-Alexandre Arlove
We describe some contact non-squeezing phenomena, first in lens spaces then in strongly order able closed prequantizations in the sense of Liu. To detect and quantify these non-squ…
-Local Flatness and Geodesics of the Legendrian Spectral Distance
Simon Allais, Pierre-Alexandre Arlove
In this article, we give an explicit computation of the order spectral selectors of a pair of -close Legendrian submanifolds belonging to an orderable isotopy class. The …
Spectral selectors on lens spaces and applications to the geometry of the group of contactomorphisms
Simon Allais, Pierre-Alexandre Arlove, Sheila Sandon
Using Givental's non-linear Maslov index we define a sequence of spectral selectors on the universal cover of the identity component of the contactomorphism group of any lens space…