Legendrians with vanishing Shelukhin-Chekanov-Hofer metric
Lukas Nakamura
TL;DR
This paper demonstrates that certain Legendrian submanifolds have a vanishing Shelukhin-Chekanov-Hofer pseudo-metric, providing counterexamples to a previous conjecture and expanding understanding of Legendrian geometry.
Contribution
It introduces the first known examples of Legendrians with vanishing Shelukhin-Chekanov-Hofer metric, using a lifting argument from Lagrangian to Legendrian submanifolds.
Findings
Existence of Legendrians with zero Shelukhin-Chekanov-Hofer metric
Counterexamples to Rosen and Zhang's conjecture
Application of Sikorav's lifting argument in contactization
Abstract
We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology