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Spectral selectors on strongly orderable contact manifolds and applications
Pierre-Alexandre Arlove
We prove that the spectral selectors introduced by the author for closed strongly orderable contact manifolds satisfy algebraic properties analogous to those of the spectral select…
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…
Spectral selectors and contact orderability
Simon Allais, Pierre-Alexandre Arlove
We study the notion of orderability of isotopy classes of Legendrian submanifolds and their universal covers, with some weaker results concerning spaces of contactomorphisms. Our m…
Geodesics of norms on the contactomorphisms group of
Pierre-Alexandre Arlove
We prove that some paths of contactomorphisms of endowed with its standard contact structure are geodesics for different norms defined on the identity…